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Abstract
Free-space quantum key distribution (QKD) systems are often designed to implement polarization-encoding protocols. Alternatively, time-bin/phase-encoding protocols are considerably more challenging to perform over a channel experiencing atmospheric turbulence. However, over the last decade, new and improved optical platforms have revived the interest in them. In this paper, we present a free-space multi-protocol receiver designed to work with three different time-bin/phase-encoding protocols highlighting its interoperability with different systems and architectures for potential satellite-based communications. We also present a detailed analysis of different experimental configurations when implementing the coherent one-way (COW) protocol in a free-space channel, as well as a polarization filtering technique showing how time-bin/phase-encoding protocols could be used for QKD applications in daylight conditions. We demonstrate secret key rates of several kbps for channels with a total 30 dB attenuation even with moderately high QBERs of ≈3.5%. Moreover, a 2.6 dB improvement in the signal to noise ratio is achieved by filtering background light in the polarization degree of freedom, a technique that could be used in daylight QKD.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Quantum key distribution (QKD), a technology to grow verifiably-secure encryption keys, has been one of the first quantum technologies to become commercially available. In its early development, QKD protocols were considered impractical to realize experimentally due to the stringent constraints imposed on optical sources, e.g. deterministic single-photon sources [1]. Since then, different protocols have been developed to overcome such stringent constraints, most notably the decoy-state BB84 protocol where secondary states are multiplexed with the signal states to provide information theoretical security in the presence of an eavesdropper [2–6].
Despite the development of such protocols, physical infrastructures, e.g. optical fiber networks, suffer from inherent losses due to the absorption, scattering and optical dispersion of silica [7] preventing the use of such protocols over optical links longer than a few hundred kilometers [8]. One solution would be to use free-space channels and suitable optical wavelengths exploiting the low absorption and scattering of the atmosphere [8] with the potential to use satellite links to reach users of quantum telecommunication networks on a global scale. However, to this day, no standardization of QKD platforms exists which translate to a wide range of protocols and architectures that could potentially be used by end users. Moreover, multi-user QKD networks, where different users could share secret keys using the same global infrastructure, are currently being explored for both fiber and satellite based platforms [9–11]. These have the potential of a heterogeneous selection of protocols among users, hence, interoperability is a key element needed by any future quantum architecture which aims to connect globally multiple users. Envisioning a satellite-based network, optical ground stations with hybrid optical configurations would be strongly desirable as they would not be constrained to use only a subset of compatible satellites but could potentially interface with multiple devices without the need of additional optical components. Moreover, such hybrid platforms could be able to maximize the secret key rate (SKR) for a given optical link by selecting a suitable quantum protocol based on operational conditions such as the presence of atmospheric turbulence, light pollution or specific orbital altitudes.
Most of the free-space QKD protocols developed over the years are primarily focused towards polarization-based architectures [12–18] due to the high transmission fidelity of atmospheric free-space channels in the polarization degree of freedom. However, recent work on novel optical platforms [19–23] have considerably simplified the technical and operational requirements of such systems, e.g. the ability to perform multimodal interferometry, the need for fewer optical and electrical components, thus renewing the interest in time-bin/phase-encoding QKD protocols.
In this paper the design and characterization of a multi-protocol free-space receiver for time-bin/phase-encoding protocols is presented, utilizing polarization routing techniques [24]. We demonstrate the performance of three different QKD protocols at 1 GHz clock rate: the coherent one-way (COW) protocol [25], the differential phase shift (DPS) protocol [26] and the time-bin decoy BB84 protocol [2–4], showing secret key rates 1.6 kbps, 64 bps, and 2.4 kbps respectively after a 30 dB channel attenuation. This design is compatible with demonstrated transmitters also capable of performing these three protocols [27–29]. We propose an original method to operate the COW protocol in free-space, which includes a adjustable variable beamsplitter (BS) that can change the splitting ratio according to the signal-to-noise ratio (SNR) measured by the optical receiver, maximizing the secret key rate. Finally, a novel method to increase the SNR in noisy environments using a polarization filtering technique is also introduced, where an increase of 2.6 dB in the SNR was measured by simply adding a polarizer and aligning the signal to the transmitting axis.
2. Methods
The optical setup of the transmitter device is reported in Fig. 1. A distributed feedback laser of 852 nm central wavelength with a 1 MHz linewidth was operated in continuous wave mode. The source’s output was fiber coupled to an intensity modulator (IM) used to pulse-carve the beam via RF modulation.
Fig. 1. Schematic representation of the optical setup of the transmitter device. A laser of 852 nm central wavelength with a 1 MHz linewidth operated in continuous wave mode is pulsed by an intensity modulator (IM) after being coupled to an isolator to limit back reflections. A phase modulator (PM) is used to modulate individual pulses according to the protocol studied. The beam intensity is then attenuated to single-photon levels via a variable optical attenuator (VOA) and a fixed 40 dB inline optical attenuator. Finally, the light is coupled to a 3x free-space beam expander via a collimation package (CP) to reduce the beam’s divergence before reaching the receiver.
To maintain a stable interference at the output, the IM voltage was controlled with a bias driver. This driver was in-built with the IM making use of an external laser source. The RF signal was a random pulse pattern at 1 GHz repetition rate generated by an arbitrary waveform generator (AWG) with 20 GHz bandwidth. The IM was then fiber coupled to an electro-optic phase modulator (PM) which was used to impart a relative phase modulation to individual laser pulses specific to each protocol studied. Reference pulses with deterministic intensity and phase modulations were also multiplexed into the signals to use for interferometric visibility estimation (see supplementary material for further details). The optical pulses were then attenuated using a variable optical attenuator (VOA) and an additional fixed inline 40 dB optical attenuator to reach single-photon level intensities. A collimation package was then used to couple the optical beam to a 3x magnifying free-space beam expander increasing its beam size and reducing its angular divergence which also improved the quality of the interference due to the size of the optical components used in the receiver device.
A schematic representation of the receiver device can be seen in Fig. 2. A 10x free-space beam expander in reverse mode collected the optical beam from the transmitter device and coupled it into the interferometer via a series of mirrors. Given the reconfigurable nature of the receiver, it is useful to divide the device into four main areas. Area I (orange shaded rectangle in Fig. 2) was the polarization manipulation zone comprising a half wave plate (HWP) and a polarizing beamsplitter (PBS). Here the input states were routed to different measurement stages according to the specific protocol studied. In particular, all pulses were routed to the interferometer when operating either the DPS or BB84 protocols, while the transmission/reflectivity for the COW protocol were chosen according to the SNR at the interferometer to optimize the SKR (see subsection 2.1 for further details). A polarization filter was also inserted to increase the SNR when simulating a noisy environment.
Fig. 2. Schematic representation of the free-space receiver device. Area I comprises a variable BS made by a half wave plate (HWP) and a polarizing beamsplitter (PBS) used to modify the polarization routing. Area III comprises an unbalanced Michelson interferometer with a 1 ns relative optical path difference. Quarter wave plates (QWPs) are placed in each arm for polarization routing. Areas II and IV constitute the measurement stages of the system. Specifically, Area II is the key generation stage when operating the COW protocol while Area IV is the detection stage when operating either the DPS or BB84 protocol. A QWP was placed in the optical path of D3 to avoid back reflections going back into the interferometer.
Area III (red shaded rectangle) comprised an unbalanced Michelson interferometer with a 1 ns relative optical path difference to allow interference of consecutive pulses, at the repetition rate of 1 GHz. Relay lenses of 1.25 cm diameter aperture were mounted to allow multi-modal interference [21] greatly improving interferometric visibility. Additionally, quarter wave plates (QWPs) were placed in each arm to further reduce polarization mode mismatch and provide absolute control over the polarization routing of the quantum states (see supplementary material for further details). Areas II and IV were the detection stages of the receiver device. Specifically, Area II was defined as the key generation stage when operating the COW protocol, while Area IV was used to detect the resulting interference of the unbalanced interferometer in Area III. Each stage included silicon single-photon avalanche diodes (Si-SPADs) and focusing lenses to maximize the coupling efficiency of the optical pulses into the active area of the detectors. Spectral filters with 10 nm FWHM bandwidth (not shown) were placed in front of the detectors to increase SNR by rejecting the ambient light background. An additional QWP was placed before detector D3 to prevent back reflections from going back into the interferometer. The SPADs used had a single-photon detection efficiency of $\approx 45$% at a 850 nm detection wavelength. D2 showed a dark count rate of 50 cps while D1 and D3 had 400 cps each. Only two SPADs at a time were used during the experiment, one fixed at position D2 and the other interchangeable between position D1 and D3 according to the protocol studied, i.e. the second detector was placed at D1 when operating the COW protocol while at D3 when operating either the DPS or BB84 protocol. In a real scenario, three SPADs would be desirable in order to avoid misaligning the system and to be able to switch between protocols effortlessly. Moreover, a 2-detector design introduces an inefficiency for the time-bin BB84 protocol [30] inevitably decreasing its performance.
The interferometric visibility was measured via multiplexed reference signals with a constant relative phase difference of $\pi$. A digital gate width of 200 ps was applied around the expected arrival time of each laser pulse to further reduce the contribution of noisy events. Valid data points were recorded and saved on a PC only when the computed visibility was above a user defined threshold value.
2.1 Variable coherent one way (COW)
Based on the optical setup for the receiver device depicted in Fig. 2, a novel method to operate the COW protocol is proposed. The final secret key length depends on how much light is directed to the key stage and the visibility of the interferometer. Ideally all the light would be directed to the key stage. Nevertheless, some photons are needed at the interferometer to overcome the noisy counts. Therefore, a compromise is needed. In this paper we propose a novel method in which a HWP is rotated in front of a PBS to effectively have a variable beam splitter. With this setup a real time optimization can be done to adjust the required light into the interferometer. This is particularly useful for variable channel such as satellite QKD, where losses vary across a single orbit pass and between different ones.
The model used for the results presented in Section 3.2 followed the same model used for standard COW and detailed in the supplementary information. The splitting ratio of the PBS was sequentially modified to study its effect on the SKR and maximum achievable distance.
2.2 Polarization filtering
Free-space QKD systems require more fine filtering techniques than fiber-based platforms due to the higher contribution of background noise. Usually, three different filtering techniques are applied: time-based, wavelength-based and space-based.
One of the advantages of not working with polarization-based protocols, is that it is possible to freely manipulate the polarized quantum states without hindering the working principles of the system. Therefore, a time-bin/phase-coding system can further filter background noise using polarization as a suitable degree of freedom. Specifically, quantum states of time-bin/phase-coding protocols have a well defined polarization while ambient noise is generally unpolarized, unless under some form of jamming attack [31,32]. Therefore, a polarization filter placed at the input of the receiver device could theoretically increment the SNR by a factor of 3 dB by suppressing half of the background noise. This technique would be beneficial in daytime conditions and would provide an extra technique to further filter the noise. This is another reason to move to time-bin/phase encoding schemes, as polarization filtering can provide an additional degree of freedom to reduce noise in over and above current techniques in space, spectral, and time filtering. On top of that, a 3 dB SNR improvement is a minimum benefit to SNR assuming the background light is unpolarized. However, scattered sunlight from the sky is indeed polarized at certain bands [33,34] and higher SNR improvements could be achieved with this polarization filtering technique if the QKD signal polarization is aligned orthogonal to dominant polarization of the scattered light at a given position in the satellite pass.
3. Results
3.1 Multi-protocol performance
The QKD receiver was tested for the three different protocols. The resulting SKRs in the asymptotic regime are shown in Fig. 3 (a) for BB84, (b) for COW, and (c) for DPS as a function of the system loss (channel and receiver). A summary of the numerical results can be seen in Table 1. Details on the model used can be found in the supplementary document.
The IM had an extinction ratio of 15 dB, which introduced an inherent QBER$_{\text {encoding}}$ contribution between 1 and 2%. Increasing the extinction ratio of the modulator would allow for even higher key rates; DPS and COW would especially benefit from this enhancement since their noise tolerance is lower than that of all other protocols. The sifted key rates are represented as dotted lines, and agree well with the experimental values while the final SKRs are computed according to the models introduced in Sec. 2. The latter are plotted for a constant 95% visibility, which explains their deviation from the experimental values at higher losses due to the higher QBER and lower visibility.
Fig. 3. SKRs in the asymptotic regime and QBERs as a function of the system loss for the decoy BB84 protocol (a), Coherent One-Way (COW) protocol (b), and Differential Phase Shift (DPS) (c) protocol. Dotted lines represent the sifted key rates, solid lines represent the secret key rates and in orange the quantum bit error rate (QBER). Data points represent experimental values. Signal-to-noise ratio (SNR) of detector D1 as a function of the total system loss with and without the polarization filter (d); solid lines are fitted to experimental values to estimate the SNR improvement. Visibility measurements are included in the appendix and explain the deviations of some data points as the model assumed a constant visibility.
Table 1. Summary results of all communication protocols evaluated at 15, 20 and 30 dB system loss. The BB84 protocol outperforms all others manly due to its higher noise tolerance. Better performing optical components would decrease the QBER, especially at low attenuation levels with a significant impact on the DPS and COW protocols.
Despite its performance, the BB84 protocol (Fig. 3 (a) presents some experimental limitations that prevent the protocol from operating at maximum efficiency. Firstly, to avoid intersymbol interference, each bit is encoded in 3 temporal bins instead of two, which lowers the bit rate to 333 MHz (for a 1 GHz repetition rate). This limitation was due to the reduced number of available detectors, i.e. two instead of three. A three detector architecture would solve this issue. Secondly, the main contribution to the QBER came from the low extinction ratio of the IM, i.e. 1.6%. The other sources of error came from the visibility with a contribution of 1.25% and from the detection timing jitter with a value of 0.5%. The model simulated a system pulsed at 1 GHz repetition rate (333 MHz bit rate) and a mean photon number (MPN) of 0.8 for the signal, 0.15 for the weak decoy and 0 for the vacuum. We found these parameters optimum for the setup, and is in accordance with other experiments [16,35,36]. However, these can change for different systems as the parameter space for a QKD system is big. The probability of sending the signal states was 70%, the probability of sending the decoy states was 20% and the remaining 10% was the probability of sending the vacuum states. The visibility was set at a constant 95% while the detectors dark counts rates were set to 300 cps with a digital gate width of 200 ps. The overall detection efficiency was set to 45% and the cumulative optical loss of the receiver device was estimated to be 3 dB.
The COW protocol (Fig. 3 (b) was operated with a 70:30 beam splitting ratio, routing 70% of the incoming light to the key stage, i.e. Area II and 30% to the interferometer, i.e. Area III. This ratio was chosen to allow sufficient states to be used for visibility estimation without reducing too much the SKR. The major advantage of COW over the other protocols is that its QBER does not depend on interferometric visibility, so lower values can be easily achieved. The COW protocol’s efficiency is lower than 0.5 since every bit is encoded with two consecutive pulses and decoy sequences do not carry information, so the bit rate, in our case, was 425 MHz for a decoy probability of 15%. The main sources contributing to the QBER were the IM extinction ratio (2.3%) and the detectors’ timing jitter (0.5%). The model simulated a system pulsed at 1 GHz repetition rate, with a MPN of 0.05 and a constant visibility of 95%. The decoy probability was set at 15% while detectors’ dark counts rates were set to 300 cps with a digital gate width of 200 ps. The overall detection efficiency was set to 45% and the cumulative optical loss of the receiver device was estimated to be 1.54 dB, which is lower than the one used for the BB84 protocol as the optical pulses were routed through a different optical path.
The main advantage of DPS (Fig. 3 (c) is its efficient use of the time bins. While COW effectively only uses less than 50% of the available bins that are used to generate the secret key and BB84 wastes 2/3 of them for this implementation, DPS make use of all of them obtaining the longest sifted key and a unit protocol efficiency. However, DPS is also the protocol with the lowest noise tolerance which is evident in the difference between the sifted and secret keys. The major contributors to the QBER were: the IM extinction ratio (1.3%), the interferometric visibility (2%) and the detectors’ timing jitter (0.5%). The model simulated a system pulsed at 1 GHz repetition rate and a MPN of 0.05 with a constant visibility of 95%. The detectors’ dark counts rates were set to 300 cps with a digital gate width of 200 ps. The overall detection efficiency was set to 45% and the cumulative optical loss of the receiver device was estimated to be 3 dB. Although DPS demonstrates a lower noise tolerance, which might prevent its implementation in high-loss scenarios, improvements to increase its resilience against noise have been proposed [37]. It is worth mentioning that security models, different from the one used here, have been presented in various works [38–40].
Referencing Table 1, it is clear that the BB84 protocol outperformed all others despite having the lowest effective bit rate. This is mainly due to the low noise tolerance of the DPS and COW protocols. Also, BB84 results would improve if a third detector is included in the system. For DPS and COW, there exist improved versions of both protocols with a higher tolerance to noise making them a suitable candidate for free-space architectures that want to reach even longer telecommunication distances.
3.2 Variable coherent one way (COW)
Table 2 shows the experimental values of the SKR and QBER for different splitting ratios $t_B$ of the COW protocol with a variable beamsplitter configuration at attenuation levels of 15, 20 and 30 dB. Maximum achievable loss is also provided for each splitting ratio value. Similarly to other configurations, the sub optimal extinction ratio of the IM introduced a systematic contribution of 2.3% to the total QBER whose minimum value was found to be no less than 3%. From the variable $t_B$ perspective, the highest sifted key rate was achieved for a 90:10 ratio. An even more unbalanced configuration, e.g. a 99:1 ratio, could potentially be used to further improve the rate. Despite the higher SKR for the 90:10 ratio, interferometric visibilities above 90% were only obtained for a maximum of 30 dB total optical loss. At lower ratios, e.g. 50:50, it was possible to achieve sufficiently high visibilities for even higher attenuation levels thus still allowing to distill positive SKRs.
Table 2. Summary results of the SKR and QBER for different splitting ratios of the COW protocol with a variable beamsplitter configuration at attenuation levels of 15, 20 and 30 dB. Despite the higher SKR for the 90:10 ratio, interferometric visibilities above 90% were only obtained for a maximum of 30 dB total optical loss.
In particular, for the 80:20 ratio, visibilities above 90% could be achieved up to 30.5 dB optical loss, up to 33.7 dB for the 70:30 ratio, up to 34.4 dB for the 60:40 ratio and up to 36 dB for the 50:50 ratio. These results demonstrate how a variable $t_B$ ratio could potentially improve the SKR when implementing the COW protocol in free-space optical transmission links where the loss profile can vary during operation.
3.3 Polarization filtering
In order to test the polarization filtering technique, two different measurements were performed: one with the polarization filter and one without it. The results are shown in Fig. 3 (d). To simulate unpolarized background noise, an incandescent light bulb was used and directed towards the collection stage of the receiver device. Number of counts with the transmitter on and with and without the filter were compared. There was an average increase of 2.6 dB in the SNR with the filter mounted. We attribute the missing 0.4 dB contribution to the misalignment produced when the optic was mounted and removed from the optical setup. Additionally, the optical setup was covered with a light absorbent material that had to be removed whenever the filter had to be put in place. This did not allow to reproduce the same level of noise for different optical attenuation levels which inevitably contributed to the sub optimal noise suppression. Nevertheless, the results show good agreement with the expected theoretical value demonstrating the benefit of using a polarization filter in the presence of unpolarized background noise.
4. Conclusion
The wide variety of existing QKD protocols and the lack of global standardization means that many of the systems developed so far are incompatible with each other. In this context, the use of QKD receivers with multi-protocol capabilities offer an advantage for systems interoperability. Moreover, time-bin/phase codifications offer the possibility of suppressing background light via polarization filtering techniques, giving a minimum increase in SNR of 3 dB, which ease the implementation of daytime QKD.
In this paper, a free-space receiver with multi-protocol capabilities demonstrated the functionality and benefit under three separate experiments. The receiver device could operate three different protocols based on time-bin or phase codifications: decoy BB84, COW, and DPS. This design could be beneficial for platforms that require to interface with multiple satellites, an important feature for early global deployment systems. It could also operate with the current free-space multi-protocol transmitters that have been demonstrated in the literature [27,28].
In addition, a new adaptive method to perform the COW protocol in free-space has been presented. The method relies on a variable beamsplitter that allows to select the optimum splitting ratio between signal and decoy states according to the SNR measured at the receiver. This could enhance the performance of satellite systems where system loss profiles of free-space channels display turbulent and time-varying conditions during operation.
Finally, a polarization filtering technique has been proposed to improve daytime QKD operations. The technique, only suitable with protocols that are not based on polarization modulation, e.g. time-bin and phase-coding, leverages polarization as a controllable degree of freedom by suppressing the contribution of unpolarized background noise. The improvement provided a 2.6 dB increase of the SNR after filtering unpolarized light, showing the additional benefit of using conventional schemes that do not rely on polarization.
This work presents a design to boost interoperability between QKD systems, and renews the interest in time-bin/phase codification schemes, due to an optimized method to efficiently operate the COW protocol and a novel filtering technique to increase the SNR a minimum of 3 dB. Moreover, work is being conducted to demonstrate scenarios where this SNR increase is higher than 3 dB. Other effects would need to be considered in a realistic satellite-to-ground scenario, mainly atmospheric dephasing and Doppler effects. Atmospheric dephasing is not a major concern for this demonstration due to the high repetition rates used. This is because having a resonance close to 1 GHz that would dephase two consecutive pulses is very unlikely [41]. On the other hand, doppler effect would affect the visibility measurements, so these would need to be compensated either ahead of time or in real time. This would add complexity to the system, however, it has been already demonstrated in the literature [42–44]. This paper aims to provide a further step towards the boost in performance of satellite QKD channels and the implementation of daytime QKD.
Funding
Engineering and Physical Sciences Research Council (EP/T001011/1); Innovate UK (TS/S009353/1); Royal Academy of Engineering (RF\201718\1746).
Acknowledgment
The author Ugo Zanforlin (ugo.zanforlin.ext@leonardo.com) is now at: Leonardo Labs, Quantum Technologies Lab - Via Tiburtina, km 12,400 - Rome 00131, Italy
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [45].
Supplemental document
See Supplement 1 for supporting content.
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