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Beating the fundamental rate-distance limit in a proof-of-principle quantum key distribution system
Shuang Wang, De-Yong He, Zhen-Qiang Yin, Feng-Yu Lu, Chao-Han Cui, Wei Chen, Zheng Zhou, Guang-Can Guo, Zheng-Fu Han
TL;DR
The paper addresses the rate–distance limit that constrains repeaterless QKD. It implements a modified TF-QKD protocol with phase stabilization and demonstrates high-visibility interference and linear-bound beating at 300 km, while identifying residual phase-drift compensation as a limitation.
Problem
Repeaterless QKD is constrained by a fundamental linear rate–distance bound, motivating experimental evidence for protocols that can surpass it.
Method
The paper implements a modified TF-QKD system using phase-locked twin fields and active phase-drift compensation over long optical fibres.
Results
At 300 km, the system achieves 96.86% mean reference-part interference visibility and 3.56% corresponding quantum-part QBER, while overcoming the linear bound.
Takeaways & Limitations
The demonstration supports the practical feasibility of TF-QKD for high-rate, long-distance QKD.
Takeaways & Limitations
At 300 km, relatively low visibility reveals a limitation of the phase-drift compensation, and further work is required to reduce channel optical error.
Abstract
from arXiv · showhide
With the help of quantum key distribution (QKD), two distant peers are able to share information-theoretically secure key bits. Increasing key rate is ultimately significant for the applications of QKD in lossy channel. However, it has proved that there is a fundamental rate-distance limit, named linear bound, which limits the performance of all existing repeaterless protocols and realizations. Surprisingly, a recently proposed protocol, called twin-field (TF) QKD can beat linear bound with no need of quantum repeaters. Here, we present the first implementation of TF-QKD protocol and demonstrate its advantage of beating linear bound at the channel distance of 300 km. In our experiment, a modified TF-QKD protocol which does not assume phase post-selection is considered, and thus higher key rate than the original one is expected. After well controlling the phase evolution of the twin fields travelling hundreds of kilometers of optical fibres, the implemented system achieves high-visibility single-photon interference, and allows stable and high-rate measurement-device-independent QKD. Our experimental demonstration and results confirm the feasibility of the TF-QKD protocol and its prominent superiority in long distance key distribution services.
Protocol
The experiment uses a four-step TF-QKD protocol in which Alice and Bob randomly select code or decoy modes, send phase-coded weak coherent states to Charlie, and estimate leakage before generating secret keys. Removing phase randomization and post-selection in code mode simplifies the system and is expected to increase the key rate.
- Alice and Bob randomly select code or decoy mode for each trial, then publicly process repeated measurements to accumulate sifted bits and estimate yields.
- In code mode, Alice and Bob send phase-coded weak coherent states to Charlie, who interferes them and announces successful phase measurements for key retention.
- In decoy mode, four intensities μ, ν1, ν2, and ν3 are randomly selected while Charlie remains unaware of the mode and announces measurement outcomes.
- The protocol uses decoy observations to bound information leakage before secret key bits are generated.
- Removing phase randomization and post-selection from code mode simplifies the experimental system and is expected to produce a higher key rate.
Implementation system of TF-QKD
The TF-QKD implementation uses phase-locked twin-field sources, time-multiplexed reference and quantum pulses, and phase encoding before Charlie performs single-photon interference. Polarization control and feedback phase modulation stabilize the interference measurement.
- Alice and Bob use symmetric source, chopper, and encoder modules, with sources phase-locked to Charlie’s laser to generate twin fields at 1550.12 nm.
- The chopper converts a continuous-wave laser into 130 ps pulses at 1 GHz and separates bright reference and quantum parts, each lasting 50 μs.
- The encoder creates four intensity levels, applies {0, π} phase coding for key bits, and generates randomized decoy intensities μ, ν1, ν2, and ν3.
- Charlie interferes Alice’s and Bob’s fields on a 50/50 beam splitter, while polarization controllers and feedback phase modulators improve and stabilize interference.
- Detector D0 clicks for phase difference 0 and D1 for phase difference π; superconducting detectors provide more than 60% efficiency with dark counts below 200 Hz.
Experimental results
The experiment addresses laser phase matching and phase drift over long fibres using optical phase locking and active feedback. The stabilized source and compensation system achieve high interference visibility, including 97.21% at 300 km.
- The implementation addresses two technical challenges: producing twin fields and compensating fast phase drift over long fibres.
- An optical phase-locked loop stabilizes the master–slave laser phase difference and produces twin fields with zero offset frequency.
- Feedback phase modulators use reference-pulse detector counts to maximize constructive and minimize destructive interference.
- At 300 km, active phase-drift compensation yields mean D0 and D1 counts of 186.66 and 2.64, respectively, corresponding to 97.21% visibility.
- Without feedback, phase drift at 300 km depends mainly on ambient vibration and remains below π rad/ms over 100 ms.
Performance of the TF-QKD system
The implemented TF-QKD system is evaluated over 100, 200, and 300 km fibre distances and compared with simulations and the linear bound. Its measured secret-key performance exceeds the linear bound at 300 km.
- Secret key rates are calculated from the observed error rate, information-leakage bound, and error-correction efficiency f = 1.15.
- The measured secret key rate exceeds the linear bound at a channel distance of 300 km.
- The experimental points fit the simulation results well after measured losses are converted to equivalent distances; 300 km corresponds to approximately 53.3 dB loss and 296 km on the plot.
Discussion
At 300 km, the implemented TF-QKD system maintained high-visibility interference and relatively stable QBER while overcoming the fundamental linear rate-distance bound. The modified protocol avoids phase randomization and post-selection, improving secret-key-rate prospects, but phase-drift compensation remains a boundary for longer distances.
- Stability: Over 1000 seconds, mean reference-part interference visibility was 96.86% and mean quantum-part QBER was 3.56%.These measurements characterize the system’s long-duration stability at 300 km.
- Stability: At the 182nd second, interference visibility and QBER reached 94.54% and 4.58%, respectively, during an abrupt vibration.The passage attributes these deviations to phase drift driven mainly by ambient vibration.
- Stability: The interference-visibility and QBER standard deviations were 0.28% and 0.23%, respectively, indicating relatively stable system performance.Abrupt ambient vibrations nevertheless produced occasional lower visibility and higher QBER.
- Protocol and significance: The modified TF-QKD code mode removes phase randomization and post-selection, further improving secret-key rate compared with original TF-QKD.The implementation also controlled twin-field phase evolution over hundreds of kilometres and achieved high-visibility single-photon interference.
- Demonstration: At 300 km, TF-QKD overcame the fundamental rate-distance limit of QKD and demonstrated a first experimental violation of the linear bound.The system used 300 km of standard single-mode fibre.
16 Appendix
The appendix calculates the key rate by bounding Eve’s information from experimentally observed yields. Finite decoy-state bounds constrain the variables used in this estimate.
- The key rate is calculated as R = Qμμ(1 − f h2(eb) − IAE).The calculation requires estimating Eve’s information on the key bits.
- The optimization uses non-negative variables x00, x10, x11, and x01 constrained by yields Yn,m.Yn,m is the yield when Alice and Bob prepare n-photon and m-photon states, respectively.
- Finite decoy-state measurements provide upper and lower bounds on Yn,m, which are used to bound the optimization variables.These bounds are applied to the finite-decoy setting before estimating Eve’s information.
- The constraints are established by linear programming while satisfying the experimentally observed yields.
The detailed experimental data
This section lists the experimental data and simulation assumptions used to characterize the system. It specifies table quantities, channel and detector parameters, and optimized decoy intensities.
- The experimental data are organized in two tables, including channel-distance and attenuation information and decoy-mode yields.
- The notation defines μ as the signal-state intensity, ν1, ν2, and ν3 as decoy-state intensities, Q as yield, and e as raw-key-bit error rate.
- The simulation models channel transmittance as η = 10^-0.018lηD, with overall measurement-device efficiency ηD = 0.305.
- The simulation assumes a dark-count rate d = 10^-7 per pulse and optical misalignment of 0.03.
- The decoy intensities are ν1 = 0.005, ν2 = 0.002, and ν3 = 10^-2.5μ, while μ is optimized at each distance.
- Experimental yields and error rates are simulated using the formulae given in the cited appendix.