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Experimental quantum key distribution beyond the repeaterless secret key capacity
M. Minder, M. Pittaluga, G. L. Roberts, M. Lucamarini, J. F. Dynes, Z. L. Yuan, A. J. Shields
TL;DR
Quantum communications are constrained by channel loss and the repeaterless secret key capacity. This paper experimentally demonstrates TF-QKD with phase-coherent signals and an intermediate untrusted node, surpassing that limit.
Problem
Propagation losses constrain quantum communication rates and range below the repeaterless secret key capacity.
Method
Alice and Bob use phase-locked lasers to prepare coherent states, whose optical fields interfere at an intermediate measuring station, with three-intensity implementations tested.
Results
At 71.1 dB loss, secure key rates reached 213.0 bit/s and 270.7 bit/s, 1.90 and 2.42 times the ideal repeaterless secret key capacity.
Takeaways & Limitations
The experiment provides the first evidence that TF-QKD can surpass the direct-link rate-loss limit and enhance quantum communication range and rate using available technology.
Takeaways & Limitations
The results are asymptotic, omit finite-size effects and long-haul real fibres, and do not establish robustness against side-channel attacks.
Abstract
from arXiv · showhide
Quantum communications promise to revolutionise the way information is exchanged and protected. Unlike their classical counterpart, they are based on dim optical pulses that cannot be amplified by conventional optical repeaters. Consequently they are heavily impaired by propagation channel losses, which confine their transmission rate and range below a theoretical limit known as repeaterless secret key capacity. Overcoming this limit with today's technology was believed to be impossible until the recent proposal of a scheme that uses phase-coherent optical signals and an auxiliary measuring station to distribute quantum information. Here we experimentally demonstrate such a scheme for the first time and over significant channel losses, in excess of 90 dB. In the high loss regime, the resulting secure key rate exceeds the repeaterless secret key capacity, a result never achieved before. This represents a major step in promoting quantum communications as a dependable resource in today's world.
EXPERIMENTAL SETUP
The experiment phase-locks Alice’s and Bob’s coherent optical fields, encodes them in high-speed pulses, and interferes them at an intermediate station after highly lossy transmission. Stable phase references, high-visibility interference, and single-photon detection support the TF-QKD implementation.
- EXPERIMENTAL SETUP: Alice’s and Bob’s coherent states interfere at Charlie’s beam splitter after traversing two highly lossy channels, requiring stable optical phase over time.Reduced detected counts under high loss make maintaining phase stability challenging.
- EXPERIMENTAL SETUP: Alice’s laser provides the phase reference and locks Bob’s laser through a service fibre and heterodyne optical phase-locked loop.The reference light is split at Alice and part is sent to Bob for phase locking.
- EXPERIMENTAL SETUP: Modifying the phase-locking reference would appear as phase noise on the main channels, but the experiment does not establish robustness against side-channel attacks on the sending modules.The authors identify side-channel robustness as requiring further scrutiny.
- EXPERIMENTAL SETUP: The encoder gain-switches slave laser diodes at 2 GHz to produce 70 ps pulses at 1548.92 nm with high extinction ratio and constant intensity.Optical injection transfers the phase of the locked reference field to each emitted pulse.
- EXPERIMENTAL SETUP: Superconducting nanowire detectors operate at 3.2 K with 22 Hz dark counts and 44% detection efficiency; D1 extracts raw-key events while D2 monitors polarization leakage.Alice and Bob minimize leakage into the unintended polarization through polarization control.
RESULTS
The experiment implements TF-QKD with phase-locked optical fields, active phase randomisation and feedback stabilisation, and measures its gain, QBER and secure key rates across high channel losses. TF-QKD exhibits square-root gain scaling and surpasses repeaterless secret key capacity experimentally while maintaining positive key rates to 90.8 dB.
- Experimental implementation: 96.4% first-order interference visibility was obtained with the optical phase-locked loop active and Alice and Bob encoding equal phases.The system actively randomises phase while preserving high-visibility interference for TF-QKD operation.
- Experimental implementation: TF-QKD uses phase-locked optical fields, phase modulators for encoding and randomisation, and feedback control to stabilise interference at Charlie.Alice and Bob lock their laser sources, generate pulses with gain-switched laser diodes, and use reference pulses to correct phase drift.
- Gain and QBER: The system QBER remains below 1.8%, with detector dark counts and feedback increasingly affecting it only above 70 dB loss.QBER combines contributions from state preparation, detector dark counts and the feedback routine.
- Gain and QBER: The double-path gain scales with the square-root of channel transmission, whereas single-path gain scales linearly with transmission loss.At a given gain, double-path TF-QKD tolerates twice the channel loss of single-path direct-link QKD.
- Secure key rates: At 71.1 dB loss, protocols in refs. and [26] reached 213.0 bit/s and 270.7 bit/s, exceeding ideal SKC0 by factors of 1.90 and 2.42.The corresponding ideal repeaterless SKC0 was 112.0 bit/s, while positive key rates remained achievable up to 90.8 dB.
- Secure key rates: At comparable channel loss, the analysed TF-QKD protocols produced key rates three orders of magnitude above QKD and six orders above MDI-QKD records.The comparison uses 71.1 dB for TF-QKD against 71.9 dB for QKD and 64.64 dB for MDI-QKD, while noting the TF-QKD results are asymptotic.
CONCLUSIONS
The experiment demonstrates TF-QKD using phase-stabilised and phase-randomised pulses, providing experimental evidence that it can surpass the direct-link rate-loss limit and extend quantum communication over 90 dB loss.
- CONCLUSIONS: TF-QKD carries quantum information in Alice’s and Bob’s optical fields, which can tolerate larger loss than photons.The paper presents this as the basis for potentially increasing quantum-communication rate and range.
- CONCLUSIONS: Phase-stabilised and phase-randomised pulses are prepared relative to a shared phase reference.The phase stabilisation uses an optical phase-locked loop, while feedback stabilises the channels to Charlie.
- CONCLUSIONS: The experiment extracts a positive key rate over a 90 dB loss link while overcoming the theoretical rate-loss limit.The reported link loss is about 20 dB larger than in previous quantum-communication tests.
- CONCLUSIONS: The proof-of-concept experiment shows that presently available technology can enhance the range and rate of quantum communications.This conclusion is stated specifically for TF-QKD.
METHODS
The generalised TF-QKD protocol prepares encoded coherent states with multiple intensities, uses an untrusted relay and decoy-state estimation, then distils a secure key through classical post-processing.
- State Preparation: Alice and Bob prepare coherent states by randomly choosing bits, bases, global phases and one of three intensities.The phase combines the global phase with bit and basis encoding; the three intensities are signal, decoy and vacuum.
- Measurement and Announcement: Charlie announces single-detector events, while TF-QKD security remains independent of whether the intermediate relay is honest.A dishonest Charlie may use any detection scheme without affecting protocol security.
- Sifting: Sifting keeps events with matching intensities and sufficiently close twin phases, exploiting TF-QKD’s symmetry under phase addition by π.The retained values form raw key bits when Charlie reports a relevant detection.
- Parameter Estimation and Key Distillation: Remaining data are disclosed for parameter estimation, decoy states estimate security quantities, and error correction plus privacy amplification produce the final key.The considered protocols use asymptotic decoy-state equations to bound vacuum and single-photon quantities.
- Key-Rate Evaluation: The protocol analyses include specific key-rate equations and practical corrections, including an extra term that lowers the rate in one protocol.For the Curty et al. protocol, the additional term makes overcoming SKC0 more difficult.
- State Preparation: Three intensities enable practical decoy-state estimation, with u = 0.02, v = 0.2 and w < 10^-5.The experiment measures all six intensity combinations and reports an SKR of 271.3 bit/s.
OPTICAL PHASE-LOCKED LOOP
A heterodyne optical phase-locked loop locks Bob’s laser to Alice’s with an 80 MHz frequency offset, allowing the slave laser to follow the master’s fluctuations while maintaining phase coherence.
- OPLL Operation: The OPLL compares the lasers’ beat signal with an 80 MHz electrical local-oscillator reference and feeds an error signal back to Bob’s laser.A beam splitter and photodiode generate the beat signal; the loop filter tunes the slave-laser emission frequency.
- OPLL Operation: When locked, Bob’s slave laser follows Alice’s free-running master laser, keeping their frequency offset constant.The heterodyne arrangement places the beat note away from DC, enabling low-frequency-noise filtering and greater robustness to intensity fluctuations.
- Figure 4: The figure combines a schematic of the locking loop with the phase-locked photodiode spectrum, whose approximately 40 dB extinction ratio indicates residual phase error.The spectrum analyser display uses an 80 MHz horizontal-axis offset.
BIT ENCODING AND PHASE RANDOMISATION
The experiment encodes bits and bases with phase modulators and adds a pseudo-random global phase; a support experiment independently verifies full phase randomisation using optical injection locking.
- Bit Encoding: Two phase modulators encode four bit/basis phases: 0, π/2, π and 3π/2.The modulators are driven by synchronised 8-bit DAC channels and a 1 GHz square wave.
- Phase Randomisation: The main experiment adds pseudo-random global phases selected from 25 evenly spaced values over [0, 2π).The phase sequence is generated from a randomly chosen 2^10-long string.
- Support Experiment: The support experiment uses a gain-switched master laser and optical injection locking to transfer fully randomised phases to both slave lasers.It removes the OPLL and active phase randomisation while retaining active phase encoding.
- Support Experiment: Interfering adjacent-clock-cycle pulses with a 500-ps asymmetric Mach-Zehnder interferometer tests the effectiveness of phase randomisation.The corresponding intensity distribution is compared with a simulation accounting for experimental imperfections.
PHASE STABILISATION FEEDBACK AND QBER MODEL
Phase feedback stabilises the interferometer by locking the relative optical phase, keeping QBER low; without feedback, phase drift produces large QBER fluctuations. The QBER model separates optical, detector-dark-count, and feedback-error contributions.
- 30.1 dB channel loss was used to evaluate QBER over time in both the main and support experiments.
- Without phase feedback, freely drifting relative optical phase causes QBER fluctuations between 0 and 50%.When QBER exceeds 50%, the figure displays the complementary value 1−QBER because of bit-flip symmetry.
- 1.8% and 1% average QBER were measured in the main and support experiments, respectively, while feedback was enabled.Disabling feedback caused large fluctuations, and re-enabling it restored low QBER.
- The feedback signal is the photon count rate recorded by detector D3.A PID controller adjusts the phase modulator’s DC offset every 10–100 ms, with the correction rate optimised for each attenuation.
- The stabilisation lock is set at the quadrature point ∆θ = π/2, where phase compensation maintains a constant count rate of C0 + C1.The D3 count model uses C0 as the count floor, C1 as interference amplitude, and ∆ϑ as the drifting phase difference.
- The QBER model includes optical error, detector dark counts, and feedback error alongside experimentally retrieved QBER and theoretical simulation.Feedback error is modelled from persistent phase misalignment caused by phase-estimation error, with one fitting parameter.
DETAILED EXPERIMENTAL RESULTS
The experiments quantify TF-QKD gains and key rates across channel attenuation, including a measured secure key rate that exceeds the ideal repeaterless bound at 71.1 dB loss.
- Q0 = 25.9 × 10−9 was the measured gain when neither user sent pulses in the main experiment.Table I reports signal and decoy gains for Alice-only, Bob-only, and joint transmissions through detector D1.
- 270.7 bit/s SKR at 71.1 dB channel loss was 2.42 times above the ideal SKC0 bound of 112.0 bit/s.