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Twin-Field Quantum Key Distribution over 511 km Optical Fiber Linking two Distant Metropolitans
Jiu-Peng Chen, Chi Zhang, Yang Liu, Cong Jiang, Wei-Jun Zhang, Zhi-Yong Han, Shi-Zhao Ma, Xiao-Long Hu, Yu-Huai Li, Hui Liu, Fei Zhou, Hai-Feng Jiang, Teng-Yun Chen, Hao Li, Li-Xing You, Zhen Wang, Xiang-Bin Wang, Qiang Zhang, Jian-Wei Pan
TL;DR
Long-haul fiber QKD without trusted relays has remained difficult because quantum states cannot be amplified and deployed fibers challenge stable interference. This work uses SNS-TF-QKD with actively odd parity pairing to distribute secure keys over 511 km, achieving a secure key rate of 3.45 × 10−8 per pulse above the absolute PLOB bound.
Problem
Long-haul fiber QKD without trusted relays has not been achieved because quantum-signal amplification is unavailable and relay-based networks require trusted stations.
Method
The experiment implements SNS-TF-QKD with actively odd parity pairing and controls independent laser wavelengths while compensating channel phase fluctuations.
Results
3.45 × 10−8 per pulse was achieved over 511 km, exceeding the absolute PLOB bound after finite-size and fluctuation analysis.
Takeaways & Limitations
The field demonstration reports secure-key distribution over a 511 km deployed fiber link connecting two distant metropolitans.
Takeaways & Limitations
Trusted-relay networks still require relay stations to be well isolated and trusted.
Abstract
from arXiv · showhide
The basic principle of quantum mechanics guarantee the unconditional security of quantum key distribution (QKD) at the cost of inability of amplification of quantum state. As a result, despite remarkable progress in worldwide metropolitan QKD networks over the past decades, long haul fiber QKD network without trustful relay has not been achieved yet. Here, through sending-or-not-sending (SNS) protocol, we complete a twin field QKD (TF-QKD) and distribute secure keys without any trusted repeater over a 511 km long haul fiber trunk linking two distant metropolitans. Our secure key rate is around 3 orders of magnitudes greater than what is expected if the previous QKD field test system over the same length were applied. The efficient quantum-state transmission and stable single-photon interference over such a long distance deployed fiber paves the way to large-scale fiber quantum networks.
INTRODUCTION
Long-haul fiber QKD is constrained by the lack of quantum amplification and trusted-relay requirements, while TF-QKD field deployment faces environmental phase-stability challenges. The experiment addresses these challenges over a 511 km deployed fiber link and reports a secure key rate above the absolute PLOB bound.
- Motivation: Quantum-state amplification is unavailable because it would enable cloning, preventing ordinary optical amplifiers from extending long-haul fiber QKD.The no-cloning constraint makes quantum-signal amplification fundamentally different from classical optical-signal amplification.
- Motivation: The longest reported QKD field test before this work was around 90 km, while trusted-relay networks require isolated and trusted relay stations.Quantum repeaters had reached only 50 km according to the introduction passages.
- Motivation: TF-QKD promises square-root scaling with channel transmittance, but previous demonstrations beyond 500 km were laboratory experiments whose practical feasibility remained unresolved.Field tests introduce environmental noise and classical-communication crosstalk, while TF-QKD additionally requires stable single-photon interference.
- Contribution: The experiment controlled independent laser wavelengths and compensated channel phase fluctuations for a 511 km ultra-low-loss fiber link connecting Qingdao and Jinan.The link included 430 km of long-haul fiber and 81 km of fiber spool, with total loss of 89.1 dB.
PROTOCOL
The experiment uses the SNS-TF-QKD protocol with actively odd parity pairing and finite-key analysis. Alice and Bob encode key-generating events in the Z basis while using other events to estimate relevant channel and phase errors.
- Protocol: The protocol combines sending-or-not-sending twin-field QKD with actively odd parity pairing for finite-key post-processing.The zig-zag approach is used to analyze finite-key effects of actively odd parity pairing.
- State preparation: Alice and Bob randomly select X or Z bases, using vacuum and two nonzero intensities in X for decoy-state analysis.The X-basis pulses have intensities 0, µ1, or µ2 with probabilities 1 − p1 − p2, p1, and p2.
- State preparation: In the Z basis, each user randomly sends a weak coherent pulse of intensity µz or sends nothing, and these events provide the final keys.The send and not-send probabilities are ϵ and 1 − ϵ.
- Event classification: A one-detector heralded event occurs when Charlie announces that only one detector clicks.Z-basis heralded events generate keys, whereas X-basis and mismatched-basis events estimate single-photon-pair yields before actively odd parity pairing.
- Error estimation and processing: Phase-selected X-basis heralded events estimate the phase-flip error rate, while actively odd parity pairing reduces the raw-key bit-error rate.The protocol applies odd-parity error rejection during post-processing to improve the key rate.
EXPERIMENT
The experiment implements SNS-TF-QKD over field-deployed fiber linking Qingdao and Jinan, with Charlie measuring in the middle and no relay in the quantum channel. Stabilization and filtering address time, phase, polarization, intensity, and crosstalk fluctuations, yielding secure key generation over the long-haul link.
- Field deployment: SNS-TF-QKD was realized between Qingdao and Jinan using field-deployed fiber, with Charlie’s measurement station positioned in Mazhan.The long-haul network contains 12 fibers, three of which were used for quantum transmission, synchronization, and wavelength calibration.
- Field deployment: The quantum channel contains no relay node, while EDFAs amplify only synchronization and wavelength-locking signals.The independent lasers are frequency-locked across the metropolitan separation using a dedicated wavelength-locking channel.
- Optical preparation: Alice and Bob use independent continuous-wave lasers locked to ULE glass cavities, with linewidths below 1 Hz for optical encoding.The encoded pulses are attenuated to the single-photon level before transmission to Charlie.
- Stabilization: 10 ps arrival-time fluctuation was achieved with feedback, compared with a 280 ps signal-pulse duration.Without feedback, ambient-temperature changes produced arrival-time shifts of up to 20 ns in one day.
- Stabilization: 0.03 rad/µs phase drift was measured in the field-deployed fiber and compensated using phase-reference pulses and post-processing.The measured rate corresponds to 17 degrees in 10 µs, while polarization drift was controlled with electric polarization controllers.
CONCLUSION
The experiment demonstrated SNS-TF-QKD over 511 km of field-deployed fiber, generating secure keys without relying on a trusted repeater. Its key rate exceeded repeater-less limits and previous field-test expectations, supporting practical long-haul fiber quantum networking.
- CONCLUSION: The work experimentally demonstrated SNS-TF-QKD with two independent lasers and proved its feasibility in a practical environment.
- CONCLUSION: The generated secure key rate was an order higher than the absolute key-rate limit of repeater-less QKD and 3 orders of magnitudes above the previous field-test expectation.The comparison concerns applying the previous QKD field-test system over the same length.
- CONCLUSION: The techniques are intended to pave the way toward long-haul fiber quantum networks and have applications in quantum repeaters and phase-based quantum-internet architectures.
- CONCLUSION: 511 km field-deployed fibers linked Jinan and Qingdao for the experimental SNS-TF-QKD demonstration.The experiment used long-haul field-deployed fibers between the two cities.
- CONCLUSION: R = 3.45 × 10−8 was achieved as the secure key rate over the 511 km field-deployed link.
THE SNS-TF-QKD PROTOCOL WITH ODD-PARITY ERROR REJECTION
The experiment uses a 4-intensity SNS-TF-QKD protocol with decoy-state estimation and actively odd-parity pairing to generate secure keys from heralded events.
- Protocol structure: The 4-intensity SNS-TF-QKD protocol forms the experimental basis, with phase-randomized coherent states and vacuum choices used across protocol windows.Alice and Bob randomly choose X or Z bases and prepare vacuum or weak coherent pulses with specified intensities.
- Post-processing: Actively odd-parity pairing with finite-key effects is applied to the raw keys, followed by key-rate evaluation using phase-flip and bit-flip error estimates.The final expression includes Shannon entropy, error-correction and privacy-amplification failure probabilities, and a security coefficient.
- Protocol structure: Z windows are simultaneous Z-basis choices, and one-detector-heralded events in these windows form effective events and raw bit strings.The corresponding effective-event bits are assembled into Alice’s and Bob’s raw strings.
- Parameter estimation: X windows use equal µ1 intensities and phase conditions, while one-detector-heralded events support decoy analysis and phase-error estimation.The phase offset ψAB may vary between time windows to optimize the key rate.
- Parameter estimation: The decoy-state method estimates lower bounds for single-photon counting rates and untagged bits from observed source-specific counting rates.The analysis defines source counts and counting rates before applying finite-key statistical bounds.
- Post-processing: The final key rate R is computed from untagged-bit counts, phase-flip errors, residual bit-flip errors, and finite-key security parameters.Chernoff bounds and smooth-entropy-based analysis are used to estimate relevant real values from observations.
SETUP OF THE EXPERIMENT
The field experiment adapts SNS-TF-QKD to deployed metropolitan fiber conditions by using dedicated fibers for quantum transmission, synchronization, and wavelength calibration.
- Field constraints: Field conditions introduce wavelength locking between separated lasers, crosstalk from adjacent fibers, phase fluctuations, and signal-arrival-time drift.These effects distinguish the deployed setting from laboratory conditions.
- System design: The experimental system was upgraded to implement field SNS-TF-QKD over the deployed fiber infrastructure.The setup is described schematically in Fig. 4.
- System design: Three of the 12 fibers in one cable were rented: one for single-photon transmission, one for clock synchronization and start-signal distribution, and one for wavelength calibration.The calibration fiber locks the optical frequency between Alice’s and Bob’s independent lasers.
- System design: Classical communication fibers carry the other signals, while EDFAs maintain their optical power approximately every 70 km.The experiment also uses the quantum fiber channel for the single-photon-level signal.
Stable independent light sources
The experiment stabilizes Alice’s and Bob’s independent lasers with PDH-locked ultrastable cavities and reduces field crosstalk through intermittent frequency calibration.
- Laser stabilization: The two cavities have different resonant frequencies, so the independent light sources require additional frequency or wavelength-difference calibration.The calibration compensates for the distinct cavity resonances.
- Field adaptation: Compared with the laboratory experiments, the field system changes the twin-field light-source operation to decrease crosstalk noise.Frequency differences are calibrated intermittently rather than continuously locked during the experiment.
- Field adaptation: A strong continuous-wave reference calibrates the wavelength before operation, is then blocked, and the two stable sources are allowed to drift freely during the experiment.The expected wavelength difference remains small because the sources are stable.
- PDH operation: The PDH scheme phase-modulates a seed laser, detects the reflected carrier–sideband beat note, demodulates it, and feeds back through slow and fast controllers.The slow feedback adjusts the cavity-mounted PZT, while the fast feedback adjusts the AOM carrier frequency.
The encoding details
The encoding system generates randomized phase and intensity patterns, adds reference pulses, and uses stabilized modulation hardware to preserve low error and encoding stability over 511 km.
- Encoding details: Alice and Bob encode pulses with phase modulators and three intensity modulators, using 16 phase values and five intensity levels.The levels include signal, weak decoy, strong decoy, vacuum, and reference intensities.
- Encoding details: The signal intensity choices are µz, µ1, µ2, and 0, corresponding respectively to signal, weak-decoy, strong-decoy, and vacuum states.Reference pulses use a separate intensity µref.
- Hardware stabilization: Five linear voltage amplifiers drive the modulators to maintain low modulation error and high encoding stability despite large required PM drive voltages.Active bias feedback and thermal isolation in a foam box further improve decoy modulation and environmental stability.
- Long-haul transmission: The attenuated signals are sent to Charlie through a total channel length of 511 km with a loss of 89.1.Superconducting nanowire detectors are used after transmission through the channel.
The field fiber links
The experiment links Alice and Bob across a 511 km deployed fiber trunk to Charlie, using separate synchronization, calibration, and QKD links. It stabilizes wavelength, phase, and noise conditions to support long-distance interference.
- Fiber link layout: Alice and Bob modulate pulses from stable continuous-wave lasers and send them to Charlie for interference.Phase and intensity modulators generate the encoded pulses.
- Fiber link layout: 511 km of ultra-low-loss G654.E fiber connects Alice, Charlie, and Bob, with more than 300 km physically separating Alice and Bob.The QKD link has 89.1 dB total loss, averaging around 0.174 dB/km.
- Synchronization and calibration: A 430 km synchronization link distributes clocks and start signals, with five EDFAs relaying them to Alice and Bob.Charlie generates 250 MHz synchronous-clock pulses and 100 kHz system-start pulses.
- Synchronization and calibration: Wavelength calibration uses a 430 km link and six EDFAs so Bob can match his independent laser wavelength to Alice’s.Bob beats received reference light with part of his own light and adjusts an AOM accordingly.
The feedback details of the system
Field vibrations and temperature fluctuations affect polarization, pulse arrival time, and interference. Real-time polarization and arrival-time feedback substantially stabilizes these quantities.
- Environmental disturbances: Ambient vibration and temperature fluctuations can change polarization and fiber delay, deteriorating single-photon interference.They can also cause the interfering pulses to stop overlapping.
- Interference stabilization: A DWDM filters classical-communication crosstalk, while polarization optics and feedback support single-photon interference at Charlie.The idle PBS beam supplies arrival-time and polarization feedback; the other beam enters the polarization-maintaining beam splitter.
- Arrival-time feedback: 20 ns is the daily peak-to-peak arrival-time variation correlated positively with temperature.The system adjusts Charlie’s synchronization-signal phase every 20 seconds to maintain the target arrival time.
- Arrival-time feedback: Less than 80 ps peak-to-peak arrival-time variation is obtained over 6 hours with feedback.The feedback acts on the synchronization signals to make Alice’s and Bob’s pulses overlap.
Detailed Experimental Results
The experiment records optical efficiencies, detection statistics, error rates, and key rates while varying the accepted phase-difference range. This range changes both detection counts and X-basis QBER, so it is searched for optimized secure key rates.
- Experimental parameters: Tab. IV reports fiber and optical-element efficiencies, including the polarization controller, DWDM, circulator, PBS, beam splitter, and SNSPDs.Transmittances are given for relevant inputs and outputs, and SNSPD measurements include PC efficiency.
- Experimental results: Tab. V summarizes total signal-pulse sending numbers and the final key rate for the best accepted phase-difference range Ds.The table is identified as the experimental-results summary.
- Data accounting: The reported statistics distinguish sent pulses, detections, valid Z-basis detections, AOPP-surviving bits, and detector-specific counts.Additional labels identify accepted Ds ranges and correct detections used to calculate X-basis error rates.
- Phase-difference selection: Different Ds ranges produce different detection counts and X-basis QBERs for decoy states µ1 and µ2.These values are listed for the 511 km fiber experiment.
- Phase-difference selection: Optimized secure key rates are obtained by searching across accepted phase-difference ranges and associated parameter values.The search is based on the detection counts and QBER results for the different Ds choices.