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Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions

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Abstract

We analyze the unidimensional (UD) continuous-variable quantum key distribution protocol in a finite size scenario under realistic conditions. The dependence of the secret key rate on realistic parameters is analyzed numerically. A method of calculating the optimal ratio to divide the data samples in order to achieve the largest secret key rate is proposed. When the data samples are large, the superiority of the UD protocol in data processing becomes apparent. It is expected that the features and methods presented in this paper will aid in the exploration of the latent capacity of the UD protocol as well as the development of further applications.

© 2017 Optical Society of America

1. Introduction

Quantum key distribution (QKD) allows two remote and legal parties, Alice and Bob, to share a common secret key in a quantum channel, which is assumed to be controlled by a potential eavesdropper Eve, and an authenticated classical channel [1,2]. As a safe and advanced communication method, its security is based on the basic principles of quantum mechanics. Unlike discrete-variable QKD, continuous-variable (CV) QKD encodes the information into continuous-spectrum quantum observables and utilizes homodyne detectors instead of single-photon detectors. During the past decade, the theory and technology of CV QKD have undergone rapid development [3–28]. It is known that CV QKD protocols based on non-classical states demonstrate better performance than those based on coherent states. However, as the coherent state is easier to generate and only requires classical telecom technologies, coherent state based protocols have developed rapidly. Prototype machines have been developed, and several field tests have been completed [29–31]. It is believed that protocols based on coherent states can be used in practical applications in near future.

A further simplified unidimensional (UD) CV QKD protocol based on coherent states has recently been proposed [32]. Nearly simultaneously to this development, UD CV QKD was realized experimentally [33,34]. This asymmetric UD coherent state protocol allows the sender, Alice, to use one modulator instead of two, thereby reducing the complexity and cost of Alice’s apparatus. However, all previous works failed to take into account the finite-size effects, which are critical to the practical security of the QKD system.

In this paper, we mainly analyze the UD CV QKD protocol in a finite size scenario under realistic conditions. Firstly, in order to lay a good foundation, an introduction to the UD protocol under realistic conditions is presented. The analytic expression for the symplectic eigenvalues, which are used to calculate the secret key rate, is derived in order to significantly reduce the calculation time. Next, the dependence of the asymptotic secret key rate on realistic parameters, which will provide a useful guide for parameter selection, is investigated. When the amount of data samples used for parameter estimation is large in the finite size scenario, the secret key rate will approach the asymptotic secret key rate.

Unlike with the symmetrical (SY) coherent state protocol [7, 13], in the UD protocol we must estimate the transmission efficiency and excess noise of one quadrature, as well as the variance of the other quadrature. It is well known that the larger the amount of data samples used for parameter estimation, the weaker the finite size effect [35]. However, taking into consideration the real-time and stability of the QKD system, taking a longer period of time to increase the total number of samples is not necessarily beneficial. In order to distill the largest secret key rate from a limited total number of samples, a method is proposed to subdivide the data samples with an optimal ratio. After comparison, we can see that the UD protocol can achieve similar performance to its SY counterpart under realistic conditions, when the excess noise is low and number of samples is large. In particular, when the amount of data samples is large, the superiority of the UD protocol in data processing emerges.

In Sec. II, the UD CV QKD protocol under realistic conditions is presented, and the security under collective attack is analyzed using the entanglement-based (EB) scheme. Section III provides the numerical analysis of the secret key rate, depending on realistic parameters such as the reconciliation efficiency, detection efficiency, and electronic noise. Section IV presents the method of calculating the optimal ratio to divide the data samples in order to achieve the largest secret key rate under Gaussian collective attack in a finite size scenario. Finally, Section V presents the conclusions.

2. Unidimensional protocol under realistic conditions

2.1 An introduction to unidimensional protocol schemes

The prepare-and-measure (PM) scheme is shown in Fig. 1(a). The sender, Alice, displaces independent coherent states produced by a laser to a Gaussian distribution in the amplitude or phase quadrature, using one amplitude or phase modulator with a modulation variance VM. Note that the variances in this paper are all normalized to shot noise units. The Gaussian-modulated quantum states form a unidimensional chain structure in phase space with a length of VM+1and a thickness of 1. Alice sends these quantum states to Bob through an untrusted quantum channel, characterized by its transmission Tx,Tyand excess noise εx,εy. On the receiver Bob’s side, a balanced homodyne detector (BHD) with efficiency η and electronic noise υe is used to measure the amplitude or phase quadrature. In realistic conditions, it is supposed that the eavesdropper Eve cannot access Bob’s apparatus. The efficiency η and electronic noise υe are phase insensitive and should be calibrated before the communication.

 figure: Fig. 1

Fig. 1 PM and EB schemes of the UD protocol under realistic conditions.

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The EB scheme, which is equivalent to the PM scheme of the UD protocol, is shown in Fig. 1(b). On Alice’s side, an Einstein-Podolsky-Rosen (EPR) state ρAB0 with variance V is utilized. Then, Alice squeezes one of its modes B0 with squeezing parameter r=lnV . We denote the output mode S. Without loss of generality, we assume that the phase quadrature is squeezed. The resulting covariance matrix γAS is

γAS=[V0V(V21)00V0(V21)/VV(V21)0V200(V21)/V01].

The mode S, with variance V2=VM+1 in the amplitude quadrature, is sent to the remote trusted party, Bob, through a phase-sensitive channel characterized by the transmission Tx,Ty and excess noise εx,εy; the covariance matrix then becomes

γAB1=[1+VM0TxVM(1+VM)1/4001+VM0CyB1TxVM(1+VM)1/40Tx(VM+1+χlinex)00CyB10VyB1],
where VyB1 is the variance of mode B1 in the phase quadrature, CyB1 is the correlation between the two modes A and B1 in the phase quadrature, and χlinex is the channel noise in the amplitude quadrature and can be expressed as χlinex=(1Tx)/Tx+εx. Because there is no modulation in the phase quadrature, the correlation CyB1 cannot be estimated.

In the EB scheme, the realistic BHD can be modeled as a beam splitter with transmission η and a perfect BHD. The electronic noise Ve of the realistic BHD can be modeled as a thermal state ρR0, which could be considered to be the reduced state obtained from an EPR state ρR0H with variance VN entering the other input port of the beam splitter. The variance VN has a relationship with υe given by VN=1+υe/(1-η). After the beam splitter, the covariance matrix γAB has the form

γAB=[1+VM0ηTxVM(1+VM)1/4001+VM0CyBηTxVM(1+VM)1/40ηTx(VM+1+χtotx)00CyB0VyB],
where χtotx=χlinex+χhom/Tx is the total noise added between Alice and Bob relative to the channel input in the amplitude quadrature, and χhom=(1η)/η+Ve/η is the total noise introduced by the realistic BHD relative to Bob’s input in the amplitude quadrature. VyB is the variance of mode B in the phase quadrature. The noiseχhom, which is phase insensitive, has the same value in both the amplitude and phase quadrature. CyB is the correlation between the two modes A and B in the phase quadrature. VyB and CyB are related to VyB1 and CyB1 as follows

VyB=η(VyB1+χhom) and CyB=CyB1η.

2.2 Security analysis

In the asymptotic limit, the collective attack has been proven to be the optimal attack [14] and the corresponding secret key rate is given by

K=βIABχBE,
where IAB is the Shannon mutual information between Alice and Bob, χBE represents the Holevo bound between Bob and Eve for reverse reconciliation, and β is the reverse reconciliation efficiency. The mutual information can be calculated by the following expression

IAB=12log2(1+VM1+χtotx).

The Holevo bound is defined as

χBE=S(ρE)S(ρExB),
where S(ρE) is the von Neumann entropy of the eavesdropper’s quantum state ρE, and S(ρExB) is the conditional von Neumann entropy. As S(ρAB1)=S(ρE)andS(ρExB)=S(ρARHxB) [13], we can rewrite χBE as

χBE=S(ρAB1)S(ρARHxB).

After an elaborate derivation, the analytical expression for the symplectic eigenvalues of the covariance matrix γAB1 is

λ1,22=12(A±A24B),
where

A=1+VyB1+VM+VyB1(εx+VM)Tx+2CyB1(1+VM)14VMTx,
B=(VyB1(1+VM)(CyB1)21+VM)(1+εxTx).

The analytical expressions for the symplectic eigenvalues λ3,4,5 of the covariance matrix γARHxB are

λ3,42=12[C±C24D],  λ5=1
where
C=A(1+υe)+((εxTx+1)(VM+2)+VMTxA)η1+εxTxη+VMTxη+υe,
D=B(1+υeη)+(1+VM)(1+εxTx)η1+εxTxη+VMTxη+υe.
The Holevo bound can be obtained by
χBE=G(λ1)+G(λ2)-G(λ3)-G(λ4),
where G(x)=(x+1)log2(x+1)xlog2x. The variables CyB1 and VyB1 have uncertainty constrained by the Heisenberg uncertainty principle as
γAB1+iΩ0,
where Ω=k=1n=2[0110].

We then obtain the parabolic equation

(CyB1C0)2VM(1+VM)χlinex1+χlinex(VyB1V0),
where V0=1Tx(1+χlinex) and C0=V0TxVM(1+VM)1/4.

The parabolic curve between CyB1 and VyB1 is shown in black in Fig. 2. The whole plane is divided into two regions by the parabolic curve, i.e., physical region and unphysical region. The region contained by the parabolic curve is the physical region, which is divided into secure and unsecure regions by the solid cyan curve. In the secure region, the secret key rate is greater than zero. In the unsecure region, the secret key rate is less than zero. In the unphysical region, the values of CyB1 and VyB1 cannot be satisfied simultaneously. For more details about the regions, refer to Ref [32].

 figure: Fig. 2

Fig. 2 Regions of the UD protocol under realistic and ideal conditions.

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In the UD protocol, the variance of phase quadrature VyB1 can be measured by switching the detection bases randomly in the experiment. For a constant value of VyB1, the value of CyB1m corresponding to the minimum secret key rate Km can be achieved by scanning all values of CyB1 in the physical region. During the scanning process, for each value of CyB1, a corresponding secret key rate should be calculated, which is time consuming. The analytical expressions for the symplectic eigenvalues are employed to shorten the computation time significantly, rather than using the positive eigenvalues of the covariance matrix iΩγ. The solid curve of CyB1m versus VyB1 is plotted with three different colors (Fig. 2). The red solid part overlaps with the parabolic curve. As the value of VyB1 increases, it separates from the parabolic curve (the green solid part). The red and green solid parts lie in the secure region, and the secret key rates Km are larger than zero; this implies that Alice and Bob can distribute the secret key safely with a rate Km without the estimation of CyB1.The blue part is in the unsecure region, and the secret key rate Km is smaller than zero. The dashed lines indicate the corresponding cases under ideal conditions. Under realistic conditions, the parameters are set to VM=3, Tx=0.1, εx=0.01, β=0.97, η=0.6, and υe=0.1, and the curves are drawn with solid lines. Under ideal conditions the parameters are set to VM=3, Tx=0.1, εx=0.01, β=1, η=1, and υe=0, and the curves are drawn with dashed lines. From Fig. 2 it is clear that the secure region is smaller under realistic conditions. To provide a more intuitive description for the secret key rate in the secure region, four three-dimensional plots are shown in Fig. 3 from different visual angles. Figure 3(a) presents a top view of the secure region. The other subfigures present side views of the secret key rates in the secure region. It should be noted that the units of all secret key rates are bits/pulse.

 figure: Fig. 3

Fig. 3 Three-dimensional plots for the secret key rates in the secure region from different visual angles.

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3. The dependence of the secret key rate on realistic parameters

From the analysis above, we can see that Alice and Bob can share the secret key Km in the UD protocol under realistic conditions. In this section, the dependence of the secret key rate on realistic parameters, including the reconciliation efficiency β, detection efficiency η, and electronic noise υe, will be analyzed in detail.

The curves for the secret key rate Km versus the phase quadrature variance VyB1 with different reconciliation efficiencies are shown in Fig. 4. The other parameters are set to VM=3,Tx=0.1,εx=0.01,η=0.6, and υe=0.1. We can see that the secret key rate decreases with the variance of VyB1, and that there exists a maximum value VymB1. When the reconciliation efficiency is higher, the tolerable maximum variance VymB1 in the phase quadrature is larger. Obviously, a higher secret key rate Kmcan be achieved with a higher reconciliation efficiency.

 figure: Fig. 4

Fig. 4 Minimum secret key rate Km versus VyB1 for different reconciliation efficiencies under realistic conditions.

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The secret key rate Km versus the phase quadrature variance VyB1 at different detection efficiencies is shown in Fig. 5(a). The other parameters are set to VM=3, Tx=0.1, β=0.97, υe=0.1, and εx=0.01. We can see that the tolerable maximum values VymB1 are nearly the same even though the detection efficiencies are different. The secret key rate Km versus the detection efficiency η is shown in detail in Fig. 5(b) (VyB1=1.004). The secret key rate increases with the detection efficiency. For a detection efficiency higher than 0.5, the improvement of the key rate is not obvious. Due to various limitations, such as the transmission loss of the devices on Bob’s side and the quantum efficiency of photodiodes, the typical detection efficiency in current experiments is around 0.6 [20, 36].

 figure: Fig. 5

Fig. 5 (a) Secret key rate Km versus the phase quadrature variance VyB1 at different detection efficiencies. (b) The secret key rate Km versus the detection efficiency η.

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The secret key rate Km versus the phase quadrature variance VyB1 for different electronic noise values is shown in Fig. 6(a). The other parameters are VM=3,T=0.1,β=0.97, η=0.6, and εx=0.01. Note that when the electrical noise is different, the tolerable maximum variance VymB1 in the phase quadrature remains nearly unchanged. The secret key rate Km versus the electronic noise is shown in detail in Fig. 6(b) (VyB1=1.004). The lower the electronic noise, the higher the secret key rate that can be achieved. However, the secret key rate Km is almost constant when the electronic noise is in the range from [0.01, 0.1]. An electronic noise of 0.1 corresponds to a weaker LO pulse, which is beneficial for suppressing the leakage from the LO pulse to the signal pulse [36,37]. In practice, 0.1 is selected as a typical electronic noise value.

 figure: Fig. 6

Fig. 6 (a) Secret key rate Km as a function of the phase quadrature variance VyB1 with different electronic noise values. (b) The secret key rate Km versus the electronic noise υe.

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From the above numerical analysis, it is evident that in order to achieve a higher secret key rate, a higher reconciliation efficiency, higher detection efficiency, and lower electronic noise are required. Currently, the highest reconciliation efficiency that can be achieved is 97% [24], and the detection efficiency in a fiber-based system is ~0.6. The typical value of the electronic noise of 0.1 is selected.

With the parameters β=0.97,η=0.6, υe=0.1, and VyB1=1+Txεx, assuming that Ty=Tx and εy=εx, the secret key rate Km as a function of the distance is presented with different excess noise values in Fig. 7. It should be noted that the modulation variance is optimized at each distance. Compared to its SY counterpart, the UD protocol is more sensitive to the excess noise. When the excess noise is low, a comparable secret key rate and transmission distance can be achieved.

 figure: Fig. 7

Fig. 7 Secret key rate versus distance in the SY and UD coherent state protocols for different excess noise values.

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4. Secret key rate in the finite size scenario

In a practical UD CV QKD protocol, the unknown parameters are estimated using finite-sized data samples. In this section, we consider the Gaussian collective attack and analyze the secret key rate in the finite-size scenario.

The secret key rate considering the finite-size effect can be written as [35, 38, 39]

Kmf=nN(βIABχBEδPEΔ(n)),
where N is the total number of signals exchanged between Alice and Bob, in which n scales the number of signals used to extract the secret keys, and Nn scales the number of the remainder of the signals for parameter estimation. χBEδPErepresents the maximum of the Holevo information compatible with the statistics, except with the probabilityδPE. Δ(n)is a correction term for the achievable mutual information in the finite case
Δ(n)7log2(2/ϵ¯)n,  n104,
where ϵ¯ is the probability of error during privacy amplification; a conservative value of ϵ¯=10-10is utilized here.

4.1 Parameter estimation

In the UD protocol, Alice modulates the coherent states in the amplitude quadrature, and Bob measures the transmitted coherent states in the same quadrature. At the same time, Bob also needs to randomly switch the detection bases to measure the phase quadrature. Alice then rejects the portion of her data corresponding to the switched bases when Bob makes public his detection bases. After this process, Alice and Bob can share two groups of correlated data samples (xAi,xBi)i=1Nl, where xA (xB) represents Alice’s data (Bob’s data) in amplitude quadrature, and lrepresents the number of Bob’s data samples in phase quadrature. The l phase quadrature data will be used to evaluate the variance of the phase quadrature VyB. From the Nl amplitude quadrature data, Alice and Bob will select m data samples to evaluate the transmission efficiency Tx and excess noise εx.

The data obtained in the amplitude quadrature is linked through the following linear equation:

xB=txxA+zx,
where tx=ηTxand zx follows a Gaussian distribution with a mean of zero and unknown variance σx2=1+ηTxεx+υe. Here, η and υe can be well-calibrated on Bob’s side. The modulation variance of the random Gaussian variable xA is VM. In the symmetrical CV QKD protocol, it has been proven that the information gained by Eve, χBEδPE, is the largest in the case of minimum channel transmittance tmin and maximum σmax2. However, in the UD protocol the information χBEδPE obtained by Eve not only depends on the variables tx and σx2, but also has a dependence on the variable VyB1. From numerical analysis, it is not difficult to prove the following inequality:
χBEVyB1|t,σ2>0.
This means that the maximum information χBEδPE eavesdropped by Eve can be calculated by substituting tx,σx2, and VyB1 with txmin,σxmax2, and VymaxB1.

Unbiased estimators t^x and σ^x2 are known for the normal linear model:

t^x=i=1mxAixBii=1mxAi2  and  σ^x2=1m2i=1m(xBit^xxAi)2
where mrepresents the number of data samples. Moreover, t^x and σ^x2 are independent estimators with the following distribution:

t^x(tx,σx2i=1mxAi2)and(m2)σ^x2σx2χ2(m2)

Unbiased estimator V^yB is known for the Gaussian distribution:

V^yB=1l1i=1l(yBiy¯B)2,
where V^yB has the following distribution:

(l1)V^yBVyB~χ2(l1).

The chi-square distribution will be approximately equal to a normal distribution when the data set is large enough. Thus, we obtain the confidence intervals (CI) with confidence level 1δPE.

CI(tx)=[t^xΔt^x,t^x+Δt^x],CI(σx2)=[σ^x2Δσ^x2,σ^x2+Δσ^x2],CI(V^yB)=[V^yBΔV^yB,V^yB+ΔV^yB],
whereΔt^x=zδPE/2σ^x2mVM, Δσ^x2=zδPE/2σ^x22m, and ΔV^yB=zδPE/2V^yB2lwithzδPE/2=2erf1(1δPE). Here, erf1(x) is the inverse function of the error function. In addition, we haveT^x=t^x2η, ε^x=σ^x21υet^x2, andV^yB1=1+V^yB1υeη. Finally, we can obtain the worst-case values forTx, εx, andVyB1.

Txmin1η(ηT^xzδPE/21+ηT^xε^x+υemVM)2,εxmaxε^x+zδPE/2(1+ηT^xε^x+υe)2ηT^xm,VymaxB1V^yB1+zδPE/2(η(V^yB11)+1+υe)2ηl.

To calculate the final secret key rate using Eq. (19), the estimated values of T^x, ε^x, and V^yB1 are substituted by their expected values E(T^x)=Tx,E(ε^x)=εx,andE(V^yB1)=VyB1. Here we assume that VyB1=1+Txεx, Ty=Tx, and εy=εx.

4.2 Determining the largest secret key rate among N total samples

It is well known that the larger the number of data samples used for parameter estimation, the less the finite-size effects. Considering the real-time stability of the CV QKD system, it is not necessarily beneficial to increase the total number of samples. Given a number of total samples N, there is a trade-off to consider in assigning them. The proportion of the total samples used for parameter evaluation should be optimized to maximize the secret key rate. In the SY coherent state protocol, when r samples are selected to evaluate the parameters, only the proportion r/N needs to be determined. However, in the UD protocol there are two parameters, m and l. Thus, not only the proportion m/N, but also the proportion l/N needs to be determined. In order to determine the largest secret key rate with Ntotal samples, a method was designed to scan the proportions of m/N and l/Nat the same time to achieve an optimal proportion (m:l:n). The scanning result can be seen in Fig. 8.

 figure: Fig. 8

Fig. 8 Secret key rate versus the proportions of m/N and l/N.

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In Fig. 8, we can see that there exists a best proportional (BP) point (red diamond) corresponding to the largest secret key rate. The coordinate of the BP point is (l/N, m/N, KmBP) = (0.19, 0.155, 2.2 × 10-3), where KmBP is the secret key rate of the BP point, i.e., the maximum secret key rate that can be achieved when the total sample is limited. In Fig. 8, the total data sample is N=109 and the optimal ratio is (0.19: 0.155: 0.655). Thus, the number of samples used to evaluate the parameters Tx and εx is m=1.9×108, the number of samples used to evaluate the parameter V^yB1 is l=1.55×108, and the number of samples used to distill the secret key is n=6.55×108. The other parameters are set to β=0.97, Tx=0.1,εx=0.01,η=0.6, υe=0.1, VyB1=1+Txεx, and VM=3.1 (optimized).

Figure 9 presents the secret key rates versus the proportions m/N and l/Nfor different total numbers of samples. From bottom to top the total number of samples is 107, 108, 109, and 1010, respectively. The other parameters are the same as in Fig. 8, except that the transmission efficiency is Tx=0.4 (corresponding to a distance of 20 km) and the optimal modulation variance is VM=6.35. With the increase in the total number of samples, the secret key rate of the BP, KmBP, also increases, and gradually approaches the secret key rate Km (red circle).

 figure: Fig. 9

Fig. 9 Secret key rates versus the proportions m/N and l/Nfor different total samples.

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Table 1 mainly shows the proportions and the secret key rate versus the total samples. The optimal proportions m/N and l/N decrease with the increase in the total number of samples. The optimal proportions of the SY protocol are also listed, and obey a similar rule to that of the UD protocol. Kf is the secret key rate of the SY coherent state protocol with optimal modulation variance VM=18.62, transmission efficiency T=0.4, and excess noise ε=0.01. The other parameters are the same as those in the UD protocol. When the total number of samples approaches infinity, the proportions approach zero, and the secret key rate Kmf (Kf) approaches Km (K); here K is the asymptotic secret key rate in the SY protocol. Comparing the secret key rates for different total samples, we can see that the secret key rate Kmf decreases more rapidly than Kf as the total samples decrease. Therefore, the UD protocol is more sensitive to the total number of samples than the SY protocol.

Tables Icon

Table 1. Optimal proportions and secret key rates versus total number of samples.

In the SY protocol, the number of random numbers used for detection base switching is a constant,N. In the UD protocol, the proportion l/N decreases with the increasing total number of samples. This means that a smaller amount of random numbers was required to switch the detection bases to measure the non-modulated phase quadrature. Furthermore, the asymmetrical base switching in the UD protocol decreases the amount of information required for the public declaration of Bob’s measurement bases and facilitates Alice’s data sifting. Therefore, the superiority of the UD protocol emerges for QKD systems with large data samples [40].

5. Conclusion

In this paper, the finite size effect of the UD continuous-variable quantum key distribution protocol is analyzed under realistic conditions. We believe that the characteristics discovered and methods proposed in this paper will aid in the exploration of the latent capacity of the unidimensional protocol, as well as the discovery of more applications sensitive to the cost of the quantum key distribution system. The composable security [41, 42] of the UD protocol will be considered in a further theoretical analysis.

Funding

The Key Project of the Ministry of Science and Technology of China (2016YFA0301403); the National Natural Science Foundation of China (NSFC) (Grants No. 11504219, No. 61378010); Shanxi 1331KSC; the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.

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18. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012). [PubMed]  

19. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012). [PubMed]  

20. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

21. X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

22. T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015). [PubMed]  

23. B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

24. D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016). [PubMed]  

25. Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

26. S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

27. P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite size analysis of measurement device independent quantum cryptography with continuous variables,” https://arxiv.org/abs/1707.04599.

28. C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable Security against Coherent Attacks,” https://arxiv.org/abs/1704.07924.

29. S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

30. P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012). [PubMed]  

31. D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016). [PubMed]  

32. V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

33. T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

34. X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

35. A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

36. X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

37. B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

38. L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

39. O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

40. Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017). [PubMed]  

41. A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015). [PubMed]  

42. A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017). [PubMed]  

References

  • View by:

  1. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
  2. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
  3. T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
  4. N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
  5. Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
    [PubMed]
  6. F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
    [PubMed]
  7. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
    [PubMed]
  8. C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
    [PubMed]
  9. A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
    [PubMed]
  10. C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).
  11. R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
    [PubMed]
  12. M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
    [PubMed]
  13. J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).
  14. R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
    [PubMed]
  15. R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
    [PubMed]
  16. A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
    [PubMed]
  17. Q. Dinh Xuan, Z. Zhang, and P. L. Voss, “A 24 km fiber-based discretely signaled continuous variable quantum key distribution system,” Opt. Express 17(26), 24244–24249 (2009).
    [PubMed]
  18. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
    [PubMed]
  19. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
    [PubMed]
  20. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
  21. X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).
  22. T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
    [PubMed]
  23. B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
  24. D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
    [PubMed]
  25. Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).
  26. S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).
  27. P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite size analysis of measurement device independent quantum cryptography with continuous variables,” https://arxiv.org/abs/1707.04599 .
  28. C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable Security against Coherent Attacks,” https://arxiv.org/abs/1704.07924 .
  29. S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).
  30. P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
    [PubMed]
  31. D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
    [PubMed]
  32. V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
  33. T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).
  34. X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).
  35. A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
  36. X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).
  37. B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).
  38. L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).
  39. O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).
  40. Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017).
    [PubMed]
  41. A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
    [PubMed]
  42. A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
    [PubMed]

2017 (4)

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017).
[PubMed]

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[PubMed]

2016 (4)

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

2015 (5)

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
[PubMed]

2014 (1)

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

2013 (2)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

2012 (5)

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

2010 (1)

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

2009 (6)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

Q. Dinh Xuan, Z. Zhang, and P. L. Voss, “A 24 km fiber-based discretely signaled continuous variable quantum key distribution system,” Opt. Express 17(26), 24244–24249 (2009).
[PubMed]

2007 (2)

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

2006 (3)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

2005 (1)

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

2004 (1)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

2003 (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

2002 (2)

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

2001 (1)

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

Acín, A.

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

Alléaume, R.

Andersen, U. L.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Assad, S. M.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Bai, Z. L.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Berta, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Bloch, M.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Bowen, W. P.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Braunstein, S. L.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Cirac, J. I.

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

Debuisschert, T.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Dinh Xuan, Q.

Djordjevic, I. B.

Du, P. Y.

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Duhme, J.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Filip, R.

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Fossier, S.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Franz, T.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Furrer, F.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

García-Patrón, R.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

Gehring, T.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Grangier, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

Grice, W.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Grosshans, F.

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

Händchen, V.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Huang, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

Huang, L. L.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Huang, P.

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

Jacobsen, C. S.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Jouguet, P.

Karpov, E.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Kunz-Jacques, S.

Lam, P. K.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Lance, A. M.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Lassen, M.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Leuchs, G.

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

Leverrier, A.

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[PubMed]

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
[PubMed]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

Levy, M.

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Li, H.

Li, Y. M.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Lin, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

Liu, W. Y.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Lloyd, S.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Lo, H. K.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Lodewyck, J.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Lougovski, P.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Lütkenhaus, N.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

Madsen, L. S.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

McLaughlin, S. W.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Navascués, M.

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

Ottaviani, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Pache, P.

Pacher, C.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Painchault, P.

Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Peng, K. C.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Pirandola, S.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Pooser, R.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Qi, B.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Qian, L.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Qu, Z.

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

Renner, R.

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

Ruppert, L.

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Schnabel, R.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Scholz, V. B.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Sharma, V.

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

Silberhorn, Ch.

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

Spedalieri, G.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Symul, T.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Thearle, O.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Tomamichel, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Tualle-Brouri, R.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Usenko, V. C.

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Villing, A.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

Voss, P. L.

Wang, P.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Wang, S. F.

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

Wang, T.

Wang, X. Y.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Weedbrook, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

Werner, R. F.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Yang, S. S.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

Zeng, G.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

Zhang, Z.

Zhou, Y.

Chin. Phys. B (1)

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

Chin. Phys. Lett. (2)

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Nat. Commun. (2)

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Nat. Photonics (2)

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

Nature (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

New J. Phys. (1)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (10)

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Phys. Rev. Lett. (12)

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
[PubMed]

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[PubMed]

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

Phys. Rev. X (1)

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Quantum Inf. Comput. (1)

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

Rev. Mod. Phys. (2)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Sci. Rep. (1)

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

Other (2)

P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite size analysis of measurement device independent quantum cryptography with continuous variables,” https://arxiv.org/abs/1707.04599 .

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable Security against Coherent Attacks,” https://arxiv.org/abs/1704.07924 .

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Figures (9)

Fig. 1
Fig. 1 PM and EB schemes of the UD protocol under realistic conditions.
Fig. 2
Fig. 2 Regions of the UD protocol under realistic and ideal conditions.
Fig. 3
Fig. 3 Three-dimensional plots for the secret key rates in the secure region from different visual angles.
Fig. 4
Fig. 4 Minimum secret key rate K m versus V y B 1 for different reconciliation efficiencies under realistic conditions.
Fig. 5
Fig. 5 (a) Secret key rate K m versus the phase quadrature variance V y B 1 at different detection efficiencies. (b) The secret key rate K m versus the detection efficiency η .
Fig. 6
Fig. 6 (a) Secret key rate K m as a function of the phase quadrature variance V y B 1 with different electronic noise values. (b) The secret key rate K m versus the electronic noise υ e .
Fig. 7
Fig. 7 Secret key rate versus distance in the SY and UD coherent state protocols for different excess noise values.
Fig. 8
Fig. 8 Secret key rate versus the proportions of m / N and l / N .
Fig. 9
Fig. 9 Secret key rates versus the proportions m / N and l / N for different total samples.

Tables (1)

Tables Icon

Table 1 Optimal proportions and secret key rates versus total number of samples.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

γ A S = [ V 0 V ( V 2 1 ) 0 0 V 0 ( V 2 1 ) / V V ( V 2 1 ) 0 V 2 0 0 ( V 2 1 ) / V 0 1 ] .
γ A B 1 = [ 1 + V M 0 T x V M ( 1 + V M ) 1 / 4 0 0 1 + V M 0 C y B 1 T x V M ( 1 + V M ) 1 / 4 0 T x ( V M + 1 + χ l i n e x ) 0 0 C y B 1 0 V y B 1 ] ,
γ A B = [ 1 + V M 0 η T x V M ( 1 + V M ) 1 / 4 0 0 1 + V M 0 C y B η T x V M ( 1 + V M ) 1 / 4 0 η T x ( V M + 1 + χ t o t x ) 0 0 C y B 0 V y B ] ,
V y B = η ( V y B 1 + χ hom )   a n d   C y B = C y B 1 η .
K = β I A B χ B E ,
I A B = 1 2 log 2 ( 1 + V M 1 + χ t o t x ) .
χ B E = S ( ρ E ) S ( ρ E x B ) ,
χ B E = S ( ρ A B 1 ) S ( ρ A R H x B ) .
λ 1 , 2 2 = 1 2 ( A ± A 2 4 B ) ,
A = 1 + V y B 1 + V M + V y B 1 ( ε x + V M ) T x + 2 C y B 1 ( 1 + V M ) 1 4 V M T x ,
B = ( V y B 1 ( 1 + V M ) ( C y B 1 ) 2 1 + V M ) ( 1 + ε x T x ) .
λ 3 , 4 2 = 1 2 [ C ± C 2 4 D ] ,     λ 5 = 1
C = A ( 1 + υ e ) + ( ( ε x T x + 1 ) ( V M + 2 ) + V M T x A ) η 1 + ε x T x η + V M T x η + υ e ,
D = B ( 1 + υ e η ) + ( 1 + V M ) ( 1 + ε x T x ) η 1 + ε x T x η + V M T x η + υ e .
χ B E = G ( λ 1 ) + G ( λ 2 ) - G ( λ 3 ) - G ( λ 4 ) ,
γ A B 1 + i Ω 0 ,
( C y B 1 C 0 ) 2 V M ( 1 + V M ) χ linex 1 + χ linex ( V y B 1 V 0 ) ,
K m f = n N ( β I A B χ B E δ P E Δ ( n ) ) ,
Δ ( n ) 7 log 2 ( 2 / ϵ ¯ ) n ,     n 10 4 ,
x B = t x x A + z x ,
χ B E V y B 1 | t , σ 2 > 0 .
t ^ x = i = 1 m x A i x B i i = 1 m x A i 2     a n d     σ ^ x 2 = 1 m 2 i = 1 m ( x B i t ^ x x A i ) 2
t ^ x ( t x , σ x 2 i = 1 m x A i 2 ) a n d ( m 2 ) σ ^ x 2 σ x 2 χ 2 ( m 2 )
V ^ y B = 1 l 1 i = 1 l ( y B i y ¯ B ) 2 ,
( l 1 ) V ^ y B V y B ~ χ 2 ( l 1 ) .
CI ( t x ) = [ t ^ x Δ t ^ x , t ^ x + Δ t ^ x ] , CI ( σ x 2 ) = [ σ ^ x 2 Δ σ ^ x 2 , σ ^ x 2 + Δ σ ^ x 2 ] , CI ( V ^ y B ) = [ V ^ y B Δ V ^ y B , V ^ y B + Δ V ^ y B ] ,
T x min 1 η ( η T ^ x z δ P E / 2 1 + η T ^ x ε ^ x + υ e m V M ) 2 , ε x max ε ^ x + z δ P E / 2 ( 1 + η T ^ x ε ^ x + υ e ) 2 η T ^ x m , V y max B 1 V ^ y B 1 + z δ P E / 2 ( η ( V ^ y B 1 1 ) + 1 + υ e ) 2 η l .

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