Field implementation of long-distance quantum key distribution over aerial fiber with fast polarization feedback

Dong-Dong Li; Song Gao; Guo-Chun Li; Lu Xue; Li-Wei Wang; Chang-Bin Lu; Yao Xiang; Zi-Yan Zhao; Long-Chuan Yan; Zhi-Yu Chen; Gang Yu; Jian-Hong Liu

doi:10.1364/OE.26.022793

¹Department of Modern Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China

²Chinese Academy of Sciences (CAS) Center for Excellence and Synergetic Innovation in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China

1. Introduction

Quantum key distribution (QKD) is a powerful way to perform private communications while enjoying unconditional security guaranteed by the fundamental principles of quantum mechanics [1–3]. QKD enables two remote parties, e.g., sender Alice and receiver Bob, to share identical keys that are not accessible to eavesdropper (Eve). Combined with the one-time pad protocol [4], the encrypted massage using these secure keys cannot be interpreted by Eve. Following the original proposal of BB84 protocol [5,6], the polarization-encoded photons are naturally chosen as the information carrier in the QKD system. Travelling along the fiber link is one of the most efficient methods to deliver the propagating photons. In fact, owing to the residual birefringence in optical fibers, the state of polarization (SOP) of the propagating photons changes over time [3], increasing the error rate during quantum communication. Fortunately, in the indoor fiber spool or the buried/ducted fibers, the vibration of SOP is not extremely fast. By employing some relatively slow polarization control system [7–10], SOP can be stabilized for a sufficiently long period in order to exchange secure keys. Hence, the polarization-encoded qubit is widely adopted in the quantum-secured networks around the world [11–16]. However, this is not always the case. Aerial fibers swinging in the wind or cables along the railway are examples of exceptions. As they become exposed to harsh environments, the SOP in these fiber links vibrates dramatically over time, because of thermal or mechanical changes [17,18]. This results in a high error rate, which compromises the performance of communication or even obstructs the distribution of secure keys. QKD in these scenarios remains a great challenge.

To overcome such limitations, we have developed a fast polarization feedback module, with which we can redress the polarization changing of the fiber link over much shorter time and recover the SOPs at the receiver end back to the original ones at the sender end. Auxiliary classical signals, which are different in wavelength from quantum signals, are employed to provide the signals for feedback control. Due to dense wavelength division multiplexing (DWDM) at the sender’s end, the classical signals co-propagate with the quantum signals in the same direction. An additional electronic polarization controller (EPC) is inserted before the two signals are de-multiplexed at the receiver. The quantum signals are guided into the single photon detectors (SPD) to extract the assigned bit information, while the classical signals go to the polarization analyzer, including a polarization-dependent beam splitter (PBS) to measure the visibility in H/V basis and another rotated PBS to measure the visibility in +/− basis. The outcome of the polarization analyzer is fed into the field programmable gate array (FPGA) to generate the electric pulse to control the EPC in a closed-loop configuration. Through several iterations, the polarization of the classical signals return to the initial state, and so do the quantum signals. As the response time is below 1 ms, our scheme works effectively in the situation of rapid polarization fluctuation, such as in the case of aerial fiber links. Remarkably, our polarization compensation system is resource-efficient and of low cost. It acts as a relatively independent module, and can be adapted to commercial QKD systems in a Plug-and-Play setting.

Using our fast polarization feedback system, we have achieved experimental demonstration for the first time, to the best of our knowledge, of polarization-encoded QKD over long-distance aerial fibers. The secure distance here exceeds 68 km, reaching more than 15 dB attenuation. After continuous operation for a duration of 16 days in the presence of strong impact of SOP from the real world, the accumulated keys are over 3 Gbits with an average secure key rate of 2 kbps. We have also achieved field test of QKD over mixed fiber link which consists of both buried cables and aerial cables.

2. Experimental challenges and solutions

The error introduced by polarization mismatch is one of the main factors in polarization-encoding QKD systems. PBS is often adopted in such systems to distinguish photons with orthogonal polarization states. The SOP changes while the photons pass through the fiber link, which increases the quantum bit error rate. The quantum bit error rate (QBER) due to the polarization mismatch of the photons with a Stokes parameter of $S_{B ob} = {(s_{0} s_{1} s_{2} s_{3})}^{T}$ can be expressed as follows [19,20]:

Q B E R_{p o l a r i z a t i o n} = (1 - Δ s_{1} - Δ s_{2}) / 4,

where

Δ s_{1}

and

Δ s_{2}

represents the change of

s_{1}

and

s_{2}

of the Stokes parameter.

Figure 1 summaries the result of our field test through the 45 km installed aerial fiber in Shanghai. Figure 1(a) presents the change in polarization as a function of time. The measurement are implemented by sending 0° linearly polarized light (H) repeatly and detecting the polarization state (indicated by the stokes parameters) at the receiver. The degree of polarization (DOP) is nearly 1 and does not decrease with time. The stokes parameters suggest that the polarization is changing fast, similar to the sinusoidal curve with a period of approximately 20 milliseconds. Figure 1(b) shows QBER introduced by the polarization vibration over the aerial fiber link in a field test in Shanghai. It suggests that the polarization changes rapidly and randomly in the aerial fiber. In the long-term view, the QBER is subjected to similar changes with the polarization. The time interval, of which the error rate is below 3.9%, is very small. So the effective time for transmitting quantum information is very short. In the short-term view, the instantaneous polarization change is also very rapid. Within 3 ms, the polarization error rate rises to 3.9%, which exceeds the preset threshold of our system and significantly reduces the quantum communication key rate. Within 5 ms, the error rate increases to 11%, which blocks quantum communication [21].

Fig. 1 Field test result through 45 km installed aerial fiber in Shanghai. (a) The change of polarization indicated by the stokes parameters. (b) QBER introduced by polarization vibration in aerial fiber.

Download Full Size | PDF

Fortunately, in the standard fiber currently used in communication, the degree of polarization (DOP) of a polarized signals does not decrease much even after travelling over long distance. Therefore, the influence of the fiber on the polarization of the quantum light can be approximated using a unitary transformation $U_{F} (t)$ [3]. The output polarization state is equivalent to applying a unitary matrix transformation to the input polarization state. It should be noted that this matrix is time-dependent. One can use a polarization controller to perform another unitary transformation $T_{P C} (t)$ to correct the polarization change in the fiber, which means that:

T_{P C} (t) = U_{F}^{- 1} (t)

Then, the output SOP is generally consistent with the original SOP. It is easy to see that the transformation matrix used for polarization compensation is also time-dependent and has the same period of variation as the fiber. When the optical fiber receives severe influence from external environmental factors, the polarization state in the fiber will change rapidly. To successfully transmit the quantum information, it is necessary to vary the polarization compensation matrix with the same period to effectively compensate for the influence of the fiber channel on the error rate.

The polarization fluctuation in the fiber is not periodic, but is a random vibration. During a short time interval $τ_{0}$ , such as 1 ms, the impact can be treated as a constant transform $U_{F} (τ_{0})$ . Through several iterations, we can get close to the inverse transformation $U_{F}^{- 1} (τ_{0})$ , which means that

T_{P C} (t) = T_{P C}^{1} (t_{1}) T_{P C}^{2} (t_{2}) \dots T_{P C}^{N} (t_{N}) = U_{F}^{- 1} (τ_{0})

All these iterations should be implemented within the interval $τ_{0}$ , which means that $t_{1} + t_{2} + \dots + t_{N} \leq τ_{0}$ . The experimentally measured time intervals are of order of 1 ms. Therefore, an urgent demand arises for ultrafast polarization compensation systems with a response time below 1 ms.

The schematic of the fast polarization feedback system we have developed is shown in Fig. 2. The central wavelength of quantum signals is 1550.12 nm. We use distributed feefback (DFB) lasers of wavelength equal to 1560.92 nm to produce the feedback signals to track the polarization changes of the fiber link. At the transmitter end, the DFB laser is used to emit light pulses at a frequency of 100 kHz. The direct output power of the DFB is about −20 dBm, and the pulse width is about 12.5 ns (FWHM). The pulses are separated by a 50:50 polarization-maintaining beam splitter (PMBS). One down arm represents signals of 0° polarization (H); the upper arm represents signals of 45° polarization (P), with a time delay of 1.6 ns and axially rotating the coupling polarization-maintaining fiber of BS1 by 45°. The feedback signals and the quantum signals are multiplexed with dense wavelength division multiplexer (DWDM) and then co-propagate in the same optical fiber. The measured isolation of the DWDM is above 32 dB. In long-distance communication, fiber resources are usually limited, and the construction and maintenance costs are expensive. With this wavelength-division-multiplexing setup, we have eliminate the extra fiber link requirement for transmitting the feedback signal, which makes our scheme cost-effective.

Fig. 2 Schematic of fast polarization feedback (FPF) system.

Download Full Size | PDF

At the receiver, another DWDM is used to separate the quantum signal and the feedback signal. The quantum signals are guided into the QKD (Bob) to perform single photon detection. The feedback signals are divided by a 10:90 beam splitter. The signals of the 10% arm goes into a PIN-type photodiode (PIN_SYN) for time synchronization detection. An variable optical attenuator (VOA) at the transmitter to automatically adjust the sending power of the feedback signals so that the receiving power at PIN_SYN is within the optimal measurement range of −45 ~-55 dBm. The signals of the 90% arm goes into a polarization analyzer to measure the polarization state. The polarization analyzer consists of a beam splitter (BS) and two PBSs. One PBS is used to measure the polarization under the H/V basis, another PBS with fiber rotated 45° in the axial direction is used to measure the polarization under the ± 45° basis. The feedback signals are detected by four PIN-type photodiodes (NR3222-1 from Wuhan Noah).The responsivity of the PIN photodiode is about 0.8A/W, and the sensitivity is better than −65dBm. The electrical signals of the five PIN detectors are detected by the high-speed acquisition card (ADC) and then fed into an FPGA. The calculation is done by the DSP with the hill-climbing algorithm to determine the voltage for EPC. After the high-voltage conversion, the 6-axis EPC is controlled.

The core requirement of the fast polarization feedback system is that the response time is fast enough to track the SOP changes and quickly complete polarization compensation before the QBER of QKD increases significantly. The feedback process does not affect the normal QKD workflow. In the real situation, the time cost for once-run must be controlled in the order of milliseconds. We use a self-developed EPC to perform polarization compensation. The EPC adopts piezoelectric ceramic to squeeze the optical fiber, controlled with high voltages of 6 channels. The piezoelectric ceramics(model of PST150/2*3/7 from Piezomechanik) have a response frequency of up to 100 kHz. Six piezoelectric ceramics are distributed along the axis of the fiber, and are arranged at an interval of 45° from each other, as shown in Fig. 2. The drive signals are generated by the FPGA and amplified by a 6-channel DAC before applied to the EPC. The maximum output voltage is approximately 90V and the measured half-wave voltage is about 40V. The EPC is compactly designed with dimensions of 122mm × 20mm × 24mm. This scheme features high speed, small size, high accuracy and economic benefits.

In the quantum stage, the feedback signal remains off, only the quantum signals are transmitted and detected. In the polarization feedback stage, the feedback signal, together with the quantum signal, are transmitted and detected. This avoids repeatedly switching the work state of the quantum signals and achieves better optical quality of the quantum pulse, such as the time jitter. Considering the isolation in our system, in the polarization feedback stage, the strong feedback signal will bring non-negligible noise (at the scale of several kcps), resulting in high error rate of quantum signals detected during this time period. This will cause a drop in the final secure key rate of QKD. Therefore, we further adopt a strategy similar to time division multiplexing to reduce this effect. During the period of polarization feedback, we discard the counts detected by QKD receiver (Bob) to ensure that the overall quantum bit error rate of the effective detection is at a low level.

We set the fast polarization feedback process to start when the error rate is higher than 3.9%. We use an optimized hill-climbing algorithm to increase the polarization feedback rate [22]. In a single run shown in Fig. 3, the DSP outputs an electrical pulse with width of 20 ns, controlling the EPC via the FPGA. After 23 microseconds, the FPGA generates four signals of 40 ns to read the error rates. If the error rate drops below the threshold of 1.5%, then the polarization feedback is ended; if the error rate is still higher than 1.5%, then the DSP cycles to change the output. The single feedback cycle takes about 27 µs. In the laboratory, when the polarization disturbance frequency is lower than 100 rad/s, the average polarization feedback can be completed within 30 cycles, which means that the total time is less than 1 ms. This high-speed system satisfies the requirements for high-speed polarization compensation in the aerial fiber links. For a typical test of 68 km aerial fiber link in the Hefei City, >43% of the polarization feedback is completed within 1 ms, >80% of the polarization feedback is completed within 2 ms, >97% of the polarization feedback is completed with more time of 5 ms.

Fig. 3 Time sequence of the fast polarization system. emif_wr denotes control pulse for EPC, emif_rd denotes reading control pulse of the error rate, and emif_cs denotes the process control pulse.

Download Full Size | PDF

3. Field test and results

Polarized qubits are used for quantum key distribution. At the transmitter, four different DFB lasers are used to generate four polarization states, horizontal/vertical/diagonal/anti-diagonal Polarization (H/V/P/N). The pulse features a width of 50 ps and a repetition frequency of 40 MHz. The currents of the lasers are modified to generate decoy states of different intensities to avoid the photon number splitting attack [23–25]. The average number of photons in the signal and decoy states is 0.6 and 0.2, respectively. The percentages of signal, decoy, and vacuum states are 50%, 25%, and 25%, respectively. At the receiver, one 50:50 BS together with two PBSs are used to achieve polarization decoding with balanced basis choice. Photon counting is performed using a gated InGaAs detector with a detection efficiency of approximately 10% and a dark count of less than 100 Hz. Another 1570 nm pulsed laser is used to synchronize Alice and Bob, with a repetition rate of 100 kHz transmitted in a parallel fiber. The data processing procedure consists of error correction based on Winnow codes with a correction efficiency of 1.2~1.6 and privacy amplification based on Toeplitz matrix to eliminate information leakage to Eve. The secure key rate can be written as [24]:

R \geq q {- Q_{μ} f (E_{μ}) H_{2} (E_{μ}) + Q_{1} [1 - H_{2} (e_{1})]}

where

q = 1 / 2

is the basis sifting efficiency,

μ

and

ν

represents the intensity of the signal state and the decoy state, respectively,

Q_{μ}

is the gain of the signal state,

E_{μ}

is the quantum bit error rate, and

e_{1}

is the error rate of the single photon state.

f (E_{μ})

is the efficiency of error correction, and

H_{2} (x)

is the binary Shannon information function.

With the help of our fast polarization feedback system, QKD is achieved with long-distance aerial fiber link. The transmitter is located in a substation in Feixi County of Hefei City. The receiver is located in another substation of Zhongxing County of Hefei City. The aerial optical fiber is installed parallel to a 500-kV high-voltage power supply grid, hanging 15 m above the ground by a tower. The average distance between adjacent towers is about 300 m. The total length of the optical cable is more than 68 km. The measured link attenuation is approximately 15 dB. After continuous operation for 16 days (2016.11.12-27), the accumulated secure key reaches 3.199 Gbits with an average key rate of 2.314 kbps. The result is shown in Fig. 4. The inserted cell shows the key rate on a particular day of 2016.11.18. The key rate is relatively high in the morning, but decreases a little in the afternoon. The average bit rate is 2.4 kbps, consistent with long-time measurement.

Fig. 4 Field test of QKD over long-distance aerial fiber link in Hefei. (a) The location of the fiber link. (b) The secure key rate of QKD.

Download Full Size | PDF

Field test of QKD in a more complex situation is also carried out in Beijing, as shown in Fig. 5. The fiber link consists of buried cables and aerial cables. The transmitter is located in Zhichunli, and the receiver is located in Changping. The aerial part extends for 14.75 km from Zhichunli to Qinghe, with the measured attenuation of 3.65 dB. The buried cable extends 25.75 km from Qinghe to Changping, with attenuation of about 6.62 dB. The total length of the link is 40.5 km and the total attenuation is about 10.3 dB. After continuous operation for 144 hours (2016.12.13-19), the accumulated secure key reaches 2.418 Gbits with an average key rate of 4.664 kbps.

Fig. 5 Field test of QKD over complex fiber link in Beijing. (a) The location of the fiber link. (b) The secure key rate of QKD.

Download Full Size | PDF

4. Conclusions

In conclusion, we have developed a fast polarization feedback system, in which the response time of one run is within 30 µs. This technique enables us to implement the first field test of long-distance quantum key distribution over the aerial fiber with polarization-encoded qubit. The maximum transmission distance exceeds 68 km with attenuation of 15 dB. The achieved secure key rate is greater than 2 kbps. Our experiments not only verified the effectiveness of the fast polarization compensation scheme, but also promoted the practical application of polarization-encoded quantum communication and extended the application of quantum communications. Our solution can also be used in other situations where the stability of fiber channels is required, such as entanglement distribution, teleportation, and coherent measurements.

Funding

The Program of Beijing Municipal Science & Technology Commission (Grant No. Z171100001217002).

Acknowledgments

We would like to thank many of our colleagues for their enlightening discussions and experimental assistance. We also express deep gratitude to the anonymous reviewers for their careful work and thoughtful suggestions that have helped to improve this paper substantially.

References

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). [CrossRef]

2. H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8(8), 595–604 (2014). [CrossRef]

3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

4. G. S. Vernam, “Cipher printing telegraph systems: for secret wire and radio telegraphic communications,” J. Am. Inst. Electr. Eng. 45, 109–115 (1926).

5. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175–179.

6. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5(1), 3–28 (1992). [CrossRef]

7. C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. 98(1), 010505 (2007). [CrossRef] [PubMed]

8. G. B. Xavier, G. Vilela de Faria, G. P. Temporão, and J. P. von der Weid, “Full polarization control for fiber optical quantum communication systems using polarization encoding,” Opt. Express 16(3), 1867–1873 (2008). [CrossRef] [PubMed]

9. G. B. Xavier, N. Walenta, G. Vilela de Faria, G. P. Temporão, N. Gisin, H. Zbinden, and J. P. von der Weid, “Experimental polarization encoded quantum key distribution over optical fibres with real-time continuous birefringence compensation,” New J. Phys. 11(4), 045015 (2009). [CrossRef]

10. Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J.-W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express 18(8), 8587–8594 (2010). [CrossRef] [PubMed]

11. T.-Y. Chen, H. Liang, Y. Liu, W.-Q. Cai, L. Ju, W.-Y. Liu, J. Wang, H. Yin, K. Chen, Z.-B. Chen, C.-Z. Peng, and J.-W. Pan, “Field test of a practical secure communication network with decoy-state quantum cryptography,” Opt. Express 17(8), 6540–6549 (2009). [CrossRef] [PubMed]

12. T.-Y. Chen, J. Wang, H. Liang, W.-Y. Liu, Y. Liu, X. Jiang, Y. Wang, X. Wan, W.-Q. Cai, L. Ju, L.-K. Chen, L.-J. Wang, Y. Gao, K. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Metropolitan all-pass and inter-city quantum communication network,” Opt. Express 18(26), 27217–27225 (2010). [CrossRef] [PubMed]

13. M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, S. Fasel, S. Fossier, M. Fürst, J. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11(7), 075001 (2009). [CrossRef]

14. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19(11), 10387–10409 (2011). [CrossRef] [PubMed]

15. J. Qiu, “Quantum communications leap out of the lab,” Nature 508(7497), 441–442 (2014). [CrossRef] [PubMed]

16. Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6(1), 011024 (2016). [CrossRef]

17. D. S. Waddy, Ping Lu, Liang Chen, and Xiaoyi Bao, “Fast state of polarization changes in aerial fiber under different climatic conditions,” IEEE Photonics Technol. Lett. 13(9), 1035–1037 (2001). [CrossRef]

18. D. S. Waddy, L. Chen, and X. Bao, “Polarization effects in aerial fibers,” Opt. Fiber Technol. 11(1), 1–19 (2005). [CrossRef]

19. R. Liu, H. Yu, J. Zan, S. Gao, L. Wang, M. Xu, J. Tao, J. Liu, Q. Chen, and Y. Zhao, “Analysis of polarization fluctuation in long-distance aerial fiber for QKD system design,” Opt. Fiber Technol. (2018). In Press.

20. Y.-Y. Ding, H. Chen, S. Wang, D.-Y. He, Z.-Q. Yin, W. Chen, Z. Zhou, G.-C. Guo, and Z.-F. Han, “Polarization variations in installed fibers and their influence on quantum key distribution systems,” Opt. Express 25(22), 27923–27936 (2017). [CrossRef] [PubMed]

21. P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85(2), 441–444 (2000). [CrossRef] [PubMed]

22. P.-Y. Tang, G.-C. Li, S. Gao, G. Yu, Y.-Q. Dai, Y. Xiang, D.-D. Li, Y.-H. Zhang, B. Wu, Z.-Y. Zhao, D.-Q. Gao, J.-H. Liu, and J. Wang, “Fast polarization feedback algorithm for quantum key distribution with aerial fiber for power grid,” Acta Opt. Sin. 38(1), 0106005 (2018). [CrossRef]

23. W. Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91(5), 057901 (2003). [CrossRef] [PubMed]

24. H. K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005). [CrossRef] [PubMed]

25. X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005). [CrossRef] [PubMed]

Field implementation of long-distance quantum key distribution over aerial fiber with fast polarization feedback

Abstract

1. Introduction

2. Experimental challenges and solutions

3. Field test and results

4. Conclusions

Funding

Acknowledgments

References

Cited By

Figures (5)

Equations (4)

Optics Express