1. Introduction

Quantum key distribution (QKD) is a method that uses quantum mechanics to ensure the secure distribution of the encrypted key [1]. It can ensure the security of key information transmission in the presence of eavesdroppers [2]. The concept of QKD was first introduced in 1984 by C. H. Bennett and G. Brassard [3]. Since its introduction, QKD has undergone rapid development and has made significant breakthroughs. According to the physical amount of key information loaded, the QKD protocol can be divided into discrete-variable quantum key distribution (DV-QKD) and continuous-variable quantum key distribution (CV-QKD). In the DV-QKD protocol, the key information is encoded on discrete variables, such as the polarization direction of a single photon in the BB84 protocol. In the CV-QKD protocol, however, key information is encoded on continuously changing physical quantities, such as quadrature components of a light field. Among them, the CV-QKD scheme has the advantages of easy detection, easy integration of equipment, and easy compatibility with classical optical communication, which has attracted people’s attention [4–6]. In recent years, CV-QKD has made breakthroughs in secure transmission distance, secret key rate (SKR), chipization and information reconciliation, and has become a competitive practical solution for QKD [7–14].

In CV-QKD, the detection side uses coherent detection techniques to extract the information encoded in the quadrature component of the light field. This technique requires a strong local oscillator (LO) to be mixed with the signal light to achieve the amplification of the signal light’s quadrature component. To achieve stable interference, the scheme of transmitted LO (TLO) was first proposed. In the TLO scheme, the LO is prepared by the transmitter laser and transmitted to the receiver. The advantage of this scheme is that the LO and the signal light come from the same laser, so the LO has the same initial phase as the signal light, and the LO can provide a stable phase reference for coherent detection [4,8,15–20].

In practical implementation, to meet the conditions of interference and isolate the LO and signal, the Asymmetric Mach-Zender interferometer (AMZI) structure is usually used to divide the initial light into the LO and the signal light to ensure the same frequency of both. However, when using single-mode (SM) optical fiber to make an interferometer, such optical fibers are susceptible to environmental influences, such as small defects in the fiber core, permanent pressure, bending, torsional and temperature change, which cause changes in the polarization state of the transmitted light, thus causing changes in the contrast degree of the interference signal (the ratio of the difference between the maximum light intensity value and the minimum light intensity value in the interference field and their sum is defined as the contrast degree, which is used to quantitatively describe the clarity of the interference fringes), especially when the polarization states of the light in the two arms of the interferometer are orthogonal, the interference phenomenon will completely disappear. Therefore, we need to use a polarization-maintaining (PM) fiber to ensure that the polarization state of the light is unchanged, so that the two light paths can interfere completely, but increases the cost of the system.

Local LO (LLO) is an alternative scheme where the LO is prepared at the receiver end and mixed with the quantum signal for coherent detection [21,10]. However, the inconsistent frequency between two lasers and random phase fluctuations lead to significant phase noise. The overall phase noise is considered to be introduced by eavesdroppers in the CV-QKD protocol, which in turn will limit the practical secure transmission distance and SKR of the LLO scheme.

Faraday mirrors are widely used in optical communication technology as passive devices capable of simultaneously changing the direction of polarization and propagation of light. In 2005, Xiaofan Mo et al. present a unidirectional intrinsically stable DV-QKD scheme that is based on Faraday-Michelson interferometer (FMI), in which ordinary mirrors are replaced with 90$^o$ Faraday mirrors [22]. In 2017, FMIs are used for the time-bin phase coding quantum state preparation in the MDI-QKD system [23]. In 2018, Shuang Wang et al. propose a high-speed Faraday-Sagnac-Michelson QKD system that can automatically compensate for the channel polarization disturbance, which largely avoids the intermittency limitations of environment mutation [24]. Recently Ref. [25] presents a novel heterodyne scheme for CVQKD, which uses FMI to make it independent of polarization drift, thus eliminating the need for dynamic polarization control.

In this paper, inspired by the FMI structure in DV-QKD, we propose a new optical architecture for CV-QKD based on the FMI structure, and finally realize an all-SM fiber-based stable TLO CV-QKD system. At the transmitter side, the initial light is divided into two paths after passing through the circulator (CIR) and beam splitter (BS), one of which has a time delay line added. The two light pulses are reflected by Faraday mirrors and then converge at the BS to realize the separation of the LO and the signal light in the time domain. At the receiving end, the time-division multiplexed pulses are divided into two identical pulses through the BS, one of which passes through the delay line so that the signal pulse is aligned with the other LO pulse, thus achieving interference. The CIR then enables the light from both arms of the BS to enter the coherent detector for coherent reception. Regardless of the fiber vibrations at the transmitter and receiver, the FMI structure enables passive compensation of the polarization, allowing for accurate coherent detection in the end. Simulation results show that the scheme can achieve a SKR of 139 kbps at 70 km. The advantage of anti-polarization disturbance can be applied in the future in complex high-vibration channel environments, such as communication cables in overhead power transmission lines.

The remainder of this paper is organized as follows. In Sec. 2, we introduce the theoretical CV-QKD protocol, as well as the traditional CV-QKD system based on the AMZI structure and our proposed CV-QKD system based on the FMI structure. In Sec. 3, we model the system and analyze the quantum efficiency and various types of noise of the two systems. In Sec. 4, we analyze the performance of the systems and calculate the excess noise of both systems to obtain the SKR. The results show that our proposed scheme achieves a small difference in SKR compared to the previous scheme, and is resistant to polarization distributions, simplifying the cost and complexity of the system.

2. CV-QKD system based on FMI structure

2.1 Theoretical CV-QKD protocol

The discrete modulation coherent state (DMCS) protocol is a commonly used CV-QKD protocol, which means that the modulation state space at the transmitting end contains only a finite number of discrete distributed coherent states, and Fig. 1 illustrates the preparation-measurement model of the DMCS CV-QKD protocol, which proceeds as follows:

 

Fig. 1. Preparation-measurement model of the DMCS CV-QKD protocol. AM: amplitude modulator; PM: phase modulator; BS: beam splitter; LO: local oscillator. Alice forms a random sequence of length $n$ and prepares $n$ coherent states. Then the coherent states are sent to Bob through the quantum channel. The quantum channel can be characterized in terms of the transmittance $T$, the excess noise $\varepsilon$. After Bob receives the coherent state, it will choose to measure a certain quadrature component at random.

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(1) Alice selects the numbers $k \in \{0,1,2,3\}$ with equal probability to form a random sequence of length $n$ and prepares $n$ coherent states according to which $\left |\alpha _k\right \rangle =\left |A e^{i(2 k+1) \pi / 4}\right \rangle$, where $A$ represents amplitude. Then the coherent states are sent to Bob through the quantum channel. we can characterize this quantum channel in terms of the transmittance $T$, the excess noise $\varepsilon$, and then the channel noise at the input of Bob is $(1+T \varepsilon )$, while from the channel input it can be expressed as $\chi _{\text {line }}=(1+T \varepsilon ) / T-1=1 / T-1+\varepsilon$.

(2) After Bob receives the coherent state, it will choose to measure a certain quadrature component at random, i.e., homodyne detection, or measure both quadrature components at the same time, i.e., heterodyne detection, and the measurements are noted as $\left \{x_B\right \}$ and $\left \{p_B\right \}$. We can characterize an actual detector by the quantum efficiency $\eta$ and the electronic noise $\varepsilon _{el}$, then the detection noise at Bob’s input is $\chi _{\mathrm {det}}$, where $\chi _{\mathrm {hom\_det}}=\left [(1-\eta )+\varepsilon _{e l}\right ] / \eta$, $\chi _{\text {het\_det }}=\left [1+(1-\eta )+2 \varepsilon _{e l}\right ] / \eta$, while the total noise from the channel input can be expressed as $\chi _{\text {tot }}=\chi _{\text {line }}+\chi _{\mathrm {det}} / T$.

(3) In the case of homodyne detection, Bob publishes the base selection for his measurement and Alice keeps only the data corresponding to the quadrature component measured by Bob; in the case of heterodyne detection, Alice keeps all data.

(4) Alice randomly selects some of the retained data (e.g., $n$/2 data) for parameter evaluation and discloses these data. Bob performs parameter estimation based on the measured data, including channel transmittance $T$, excess noise $\varepsilon$, and modulation variance $V_{A}$, and then evaluates the SKR based on these parameters. If the SKR is less than zero, this key distribution is terminated and resent.

(5) Alice and Bob perform data post-processing on the remaining data, including data negotiation and secrecy enhancement, and finally obtain $m$-bit identical security keys.

Since this protocol uses discrete modulation, its reconciliation efficiency $\beta$ can be high even when the signal-to-noise ratio at the receiver side is close to 0 [26]. This is very helpful to improve the secure transmission distance of the protocol.

2.2 Previous CV-QKD system via AMZI structure

As shown in Fig. 2, the traditional CV-QKD system uses the AMZI structure at the receiver end to achieve interference, but due to the different optical ranges of the long and short arms and the birefringence effect in the fiber, the polarization state of the two light paths will change in the propagation path, resulting in the final incomplete interference, thus affecting the extraction of information. Specifically, the optical fiber will be subject to external forces during the actual production process, resulting in uneven thickness or bending of the fiber, and the two mutually perpendicular polarization modes will no longer propagate at the same speed. When the fiber is subjected to any external disturbances, the polarization state of light becomes haphazard when transmitted in a conventional fiber.

 

Fig. 2. The scheme diagram of the CV-QKD system based on AMZI structure. AM: amplitude modulator; PM: phase modulator; BS: beam splitter; LO: local oscillator; DL: delay line; VOA: variable optical attenuator; PBS: polarization beam splitter; BHD: balance homodyne detector. The laser generates continuous light, which is modulated by AM and turned into light pulses. The BS divides the light pulses into LO and signal light, where the signal light is modulated by PM for phase information. The VOA is used to attenuate the light.

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To overcome the above problems, PM fiber is usually used because it eliminate the effect of stress on the polarization state of incident light by designing the fiber geometry to produce a stronger birefringence. In addition, traditional CV-QKD systems generally use a polarization controller (PC) to solve this problem. However, both PC and PM fibers increase the cost and complexity of the system.

2.3 CV-QKD system based on FMI structure

To address the above issues, we propose a new optical architecture for CV-QKD based on the FMI structure, and finally realize an all-SM fiber-based stable CV-QKD system. The process is as follows and the scheme diagram of the whole system is shown in Fig. 3.

 

Fig. 3. The scheme diagram of the CV-QKD system based on FMI structure. AM: amplitude modulator; PM: phase modulator; FM: Faraday mirror; BS: beam splitter; DL: delay line; CIR: circulator; VOA: variable optical attenuator; BHD: balance homodyne detector. The unmodulated optical pulse signal is input to the BS and divided into signal light and LO, and the LO is transmitted to the Faraday mirror 1 and reflected, while the signal light is passed through the delay line composed of SM fiber. The two reflected pulses are then superimposed in the BS to output the time division multiplexed pulses. Then the pulses are transmitted through the channel and divided into two identical pulses at the receiving end through the BS, one of which is passed through the delay line, so that the signal pulse is aligned with the other LO pulse.

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(1) The unmodulated optical pulse signal is input to the BS and divided into signal light and LO, and the LO is transmitted to the Faraday mirror 1 and reflected, while the signal light is passed through an optical fiber delay line composed of SM fiber, so that the signal light is located in the middle of the adjacent LOs.

(2) The random number generation module generates the random number voltage signal, and the voltage signal is amplified by the radio frequency amplifier module as the modulation signal of the phase modulator.

(3) After the modulation is completed, the signal is transmitted to the Faraday mirror 2 and then reflected, and the two reflected pulses are then superimposed in the BS to output the time division multiplexed signal.

(4) Then the time division multiplexed signal is transmitted through the channel and divided into two identical pulses at the receiving end through the BS, one of which is passed through the delay line, so that the signal pulse is aligned with the other LO pulse, and the two pulses are reflected through Faraday mirrors 3 and 4, and then interfered in the BS.

The timing diagram of the long and short arm pulses of the FMI structure is shown in Fig. 4. It is worth mentioning that the time-delay scheme is used to separate the LO from the signal instead of the sequence in order to ensure that the LO and the signal have the same initial phase.

 

Fig. 4. The timing diagram of the long and short arm pulses. The LO is transmitted to the Faraday mirror and reflected, while the signal light is passed through an optical fiber delay line composed of SM fiber, so that the signal light is located in the middle of the adjacent LO.

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In contrast to the conventional solution, we compared three mainstream interferometer structures and finally chose the FMI structure, as shown in Fig. 5. Among them, both the AMZI structure and the Sagnac structure need to use PM fiber to overcome the problem of different polarizations of the two paths caused by the different optical ranges. But the FMI structure can passively compensate for polarization. A Faraday mirror is a combination of a $45^o$ Faraday rotating mirror and an ordinary mirror, and its Jones matrix is given by

 

Fig. 5. (a) Mach-zender structure. (b) Sagnac structure. (c) Faraday–Michelson structure. BS: beam splitter; FM: Faraday mirror. The red line indicates polarization-maintaining (PM) fiber and the yellow line indicates single-mode (SM) fiber. Both the AMZI structure and the Sagnac structure need to use a PM fiber to overcome the problem of different polarizations of the two paths caused by the different optical ranges. But the FMI structure can passively compensate for polarization and only SM fiber is used.

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When light passes through a birefringence medium and a Faraday mirror, the forward and backward transmission matrices can be expressed as:

3. System model analysis

In the structure of FMI, the whole key distribution process can be represented by $y=tx+\varepsilon _{n}$. where $y$ is the received signal, $x$ is the transmitted signal, and $\varepsilon _{n}$ is the noise, $t$ is the attenuation. In the above structure, $x$ is loaded with the key information by four-state modulation. After getting $y$, Bob negotiates with Alice to finally obtain the key. The attenuation $t$ and noise $\varepsilon _{n}$ are the key parameters that affect the overall performance of this system.

The attenuation $t$ consists of two parts: channel transmittance $T$ and quantum efficiency $\eta$ at the receiving end, which can be written as $t = \sqrt {T \eta }$. The channel transmittance represents the loss in the actual fiber transmission process, and the conventional transmittance calculation formula is $T = 10^{(-L\alpha )}$, where $\alpha$ represents the attenuation coefficient per kilometer of fiber, typically $0.2$ dB/km, and $L$ represents the transmission distance. This part is attributed to eavesdropper splitting in the theoretical model and is uncontrollable, and we will exclude the amount of information represented by this part completely in the parameter evaluation. While the quantum efficiency $\eta$ at the receiving end is caused by imperfections at the detector side, it is controllable and can be improved by enhancing the detector performance.

On the other hand, the noise can be divided into system excess noise, shot noise and electronic noise, which can be expressed as $\varepsilon _{n}= \varepsilon _{excess} + \varepsilon _{shot} + \varepsilon _{el}$, where shot noise is the inherent noise under CV-QKD coherent detection, and its power magnitude is completely determined by the LO’s power. The electronic noise is determined by the actual detector used and usually originates from the dark current of the photodiode and the thermal noise of the amplifier chip. The excess noise originates from channel introduced and internal system noise, which is attributed to the eavesdropper in the theoretical model and is uncontrollable.

Since the attenuation of the channel, shot noise and electronic noise are the same in any optical structure system, we focus on the quantum detection efficiency and the system excess noise under different optical structures.

3.1 Quantum efficiency

The conventional CV-QKD system based on AMZI structure is shown in Fig. 2, and its quantum efficiency represents the loss of the optical signal at the receiving end, which is sourced from the natural loss of the PBS, the loss of the BS, and the finite responsiveness of the photodiode, so the quantum efficiency of the AMZI structure can be expressed as

While the CV-QKD system based on the FMI structure is shown in Fig. 3, where the quantum efficiency is influenced by CIR and BS. Since the light passes through these devices twice, the attenuation is also twice. So the quantum efficiency of the FMI structure can be expressed as

Similarly, with conventional device parameters, the quantum efficiency is evaluated as $\eta _{\rm {FMI}} = 0.3467$, contributed by the BS with a 1-dB insert loss, the CIR with a 0.8-dB insert loss and the 350-MHz balanced detector with 1-dB loss. Due to the round-trip structure, $\eta _{\rm {BS}}$ and $\eta _{\rm {CIR}}$ are calculated twice. Since the Wiener process has the Markov property which means the change after any point is only related to the value taken at this point and not to the value taken before, we simulate the angular deviation varying at a uniform rate and the Wiener process, representing the effect of fixed external vibrations and irregular perturbations such as temperature on the polarization state, respectively. As shown in Fig. 6, the quantum efficiency of the AMZI structure varies between the maximum and minimum values with time, while the quantum efficiency of the FMI structure is stable under any perturbation.

 

Fig. 6. Quantum efficiency in AMZI structure and FMI structure. The quantum efficiency of the AMZI structure varies between the maximum and minimum values with time, while the value of the quantum efficiency of the FMI structure is stable.

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Although the quantum efficiency of the AMZI structure can be stabilized at a higher value than that of the FMI structure by controlling the polarization state change through the PC, the CV-QKD system based on the FMI structure reduces one dynamic PC which is an active device, and the rest of the devices are passive, which is cheaper and can ensure complete resistance to polarization changes at the same time.

3.2 Noise introduced by imperfect PC

As mentioned above, in a CVQKD system based on AMZI structure, a PC is usually required to control the polarization direction so that the LO and the signal interfere perfectly. However, in practical experiments, imperfect PC introduces noise and makes the interference incomplete.

We assume that the angle between the polarization direction of the LO and the signal is $\delta$, and the noise introduced by imperfect interference can be expressed as

3.3 Photon-leakage noise from LO

In the TLO CV-QKD scheme, the photons leaking from the LO cause additional excess noise. In practice, the generation of optical pulses is always limited by a finite extinction ratio $R_e$, which is defined as the ratio of the high level to the low level of the optical pulse

For AMZI structure, we can further isolate LO and signal light by polarization multiplexing, so $R_e$ can be further enhanced to $R_e + R_{po}$, thus the photon leakage noise can be expressed as

Usually PBS can achieve a polarization extinction ratio of 30 dB, so the noise can be reduced by 3 orders of magnitude as shown in Fig. 7. However, the FMI structure requires a higher extinction ratio for generation of optical pulses because only time-division multiplexing is used for isolation. With the use of optical switches, we can achieve extinction ratios of up to 100 dB. This does not contradict our original intention of reducing the system cost, since the increased cost at the transmitter side can be fully offset by the reduced cost at the receiver side of our scheme by considering a one-transmitter-multiple-receiver application in the access network.

 

Fig. 7. The curve of Photon-leakage noise from LO with extinction ratio. Since PBS can usually achieve a polarization extinction ratio of 30 dB, the noise of AMZI structure can be reduced by 3 orders of magnitude.

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3.4 Noise introduced by Faraday mirror rotation bias

In our proposed scheme, an ideal Faraday mirror can rotate the polarization direction by 90$^{\circ }$, but in the actual experiment we need to consider the imperfection of the device. If the Faraday mirror is not able to rotate the polarization direction by 90$^{\circ }$ precisely, the phase deviation of the two polarization directions of the light will be inconsistent, resulting in the polarization directions of the LO and the signal light will be inconsistent, thus affecting the interference. This is one of the difficulties in conducting experiments. We assume that the deflection error angle of the imperfect Faraday mirror is $\Delta \theta$, and the Jones matrix of the Faraday mirror is written as [27]

We assume that $\hat {\alpha }_H$ and $\hat {\alpha }_V$ represent the ideal horizontal and vertical polarization states of light, respectively, and $\hat {\alpha }_H{\prime }$ and $\hat {\alpha }_V{\prime }$ denote the actual horizontal and vertical polarization states of light, then

Since the value of $\Delta \theta$ is close to 0, the above equation can be approximated as

We assume that the incident light is linearly polarized in the horizontal direction, after the Faraday mirror reflection, the polarization state of the light is no longer completely vertically polarized, so that there will be a loss of photon state when interfering in the vertical direction, and the photon number operator in the actual case is

Correspondingly, the modulation variance of the actual system can be expressed as

 

Fig. 8. The curve of noise with angular deflection of imperfect Faraday mirror. As the deflection error angle of the imperfect Faraday reflector increases, the effect of the interference is affected, which in turn increases the noise.

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3.5 Noise introduced by CIR

In addition, since the FMI structure we use introduces a CIR, which leads to more excess noise due to the natural loss of the device. We denote the ratio of the input optical power of port1 to the output optical power of port3 when port2 is terminated and there is no reflection ratio by $d_{13}$, then the noise introduced by the CIR can be expressed as [28]

Similarly, the AMZI structure does not contain a CIR, so it does not need to analyze this noise. Table 1 lists the noise components of the two structures.

Table 1. The noise components of the two structures.

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4. Performance analysis

4.1 Excess noise

As shown in Table 1, The total excess noise in AMZI structure is expressed as

Based on the above analysis, we set $V_A = 0.5$, $\delta = 1^\circ$, $R_e = 100$dB, $R_{po} = 30$dB, $\alpha _{\rm {LO}} = 0.7\times 10^4$, $\Delta \theta = 1^\circ$, and $d_{13} = 60$dB, and then obtained each noise value as $\varepsilon _{\rm {LE}\hbox{-}{\rm AMZI}} = 10^{-5}$, $\varepsilon _{\rm {PC}} = 7.6\times 10^{-5}$, $\varepsilon _{\rm {LE}\hbox{-}{\rm FMI}} = 0.01$, $\varepsilon _{\rm {FM}} = 6\times 10^{-4}$ and $\varepsilon _{\rm {CIR}} = 5\times 10^{-7}$. For $\varepsilon _{rest}$ of both systems, we set a uniform value of 0.002. Due to the instability of the values of $\delta$ and $\Delta \theta$, we present multiple sampling points as shown in Fig. 9.

 

Fig. 9. The excess noise in the AMZI structure and the FMI structure. The blue dots indicate the excess noise of the CV-QKD system based on the AMZI structure. The red dots indicate the excess noise of the CV-QKD system based on the FMI structure.

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It can be seen that our scheme is close to the conventional scheme in terms of excess noise, but we can passively resist polarization disturbances and do not need a PC for real-time control.

4.2 Secret key rate

Based on the above system model, we can calculate the SKR that can be achieved by the CV-QKD system based on the FMI structure and the AMZI structure as shown in Fig. 10. The formula for calculating the SKR is shown in the Appendix. The parameters are selected as shown in Table 2. Here we have analyzed how the AMZI structure would be affected without the use of a polarization-maintaining fiber in order to control a single variable illustrating the comparison of the two scenarios, in particular the change in the quantum efficiency. For the AMZI structure, the SKR is unstable due to the unstable quantum efficiency, while the FMI structure can maintain a more stable key generation.

 

Fig. 10. The SKR that can be achieved by the CV-QKD system based on the AMZI structure and the FMI structure at different distances. $\eta$ denotes quantum efficiency, which changes due to changes in the polarization state without a PC.

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Table 2. Parameters in CV-QKD system.

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In addition, we analyze multiple sample points as shown in Fig. 11. Our proposed scheme can not only achieve results close to those of traditional scheme, but also under the complex environmental perturbation, AMZI has no way to code without PC or its performance is not satisfactory, while FMI can code. The sinusoidal distribution simulates the effect of a fixed external vibration on the change of polarization in an optical fiber. Wiener processes simulate irregular perturbations such as temperature.

 

Fig. 11. The SKR that can be achieved by the CV-QKD system based on the AMZI structure and the FMI structure at different rates of polarization change. Here 1 second corresponds to 50 sampling points. The distance is set to 70 km, and $\omega$ denotes the frequency of uniform changes in $\eta _{\rm {P(t)}}$. We simulate the angular deviation varying at a uniform rate and the Wiener process, representing the effect of fixed external vibrations and irregular perturbations such as temperature on the polarization state, respectively.

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4.3 Discussion

It is worth noting that there are still some issues that need to be addressed in the practical implementation. In order to achieve a high extinction ratio, we usually need to use optical switches or cascaded AMs. If the polarization multiplexing scheme is used, the need for high extinction ratio can be solved, but it is necessary to replace one of the FMs in the round-trip structure with a reflecting mirror (RM), which will make the interference effect unstable because the RM cannot passively compensate for the polarization. In addition, the length of the delay line needs to be precisely controlled in the experiment so that LO and signal light can be aligned.

One of the application scenarios we envision is that this structure can withstand severe weather in complex high-vibration channel environments, such as communication cables in overhead power transmission lines. In addition, inspired by Ref. [29], we can make a hybrid optical platform by adding a switching module at the front end of the detector to combine the DV-QKD and CV-QKD system technologies, which can be used to optimize performance in reconfigurable optical networks by selecting QKD protocols based on link parameters.

Our theoretical analysis and experiments on the structure of the FMI are matched, and its anti-interference performance has been fully verified in DV-QKD system. We will further verify it through experiments in the future.

Both the CV-QKD FMI structure and DV-QKD FMI structure have the same advantages and disadvantages. The advantage is that by using the FMI structure, a single-mode fiber can be used instead of a polarization- maintaining fiber, which reduces the cost and improves the stability of the system. It can passively realize the polarization alignment of two beams of light. In contrast, the polarization in the AMZI structure requires an active device for alignment, and poor alignment affects the quantum efficiency at the receiver. The disadvantage is that the two ends cannot be strictly symmetric in the experiment, which makes the interference effect is not able to reach the ideal 100%. To address this problem, Shuang Wang et al. proposed a Faraday-Sagnac-Michelson interferometer structure to further improve the interference effect [24]. And this structure can be used in our subsequent analysis.

5. Conclusion

In this paper, we propose the first CV-QKD system scheme based on the FMI structure, using the SM fiber-based FMI structure instead of the AMZI structure based on the PM fiber, and finally realize an all-SM fiber-based TLO CV-QKD system. By building a noise model, we analyze the performance and the advantages of the system against polarization disturbances. The final simulation results show that under the complex environmental perturbation, AMZI has no way to code without PC or its performance is not satisfactory. In addition, the theoretical SKR of our proposed scheme can reach 139 kbps at 70 km, which can further improve the stability and robustness of CV-QKD in the real environment and provide technical support for the next-generation QKD high stability network.