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Provably-Secure and High-Rate Quantum Key Distribution with Time-Bin Qudits
Nurul T. Islam, Charles Ci Wen Lim, Clinton Cahall, Jungsang Kim, Daniel J. Gauthier
TL;DR
At low-loss channels, detector saturation limits secret key rates in QKD systems. This paper develops a prepare-and-measure, d = 4 time-bin QKD system with phase-state measurements and reports a 26.2 Mbits/s secret key rate at 4 dB channel loss.
Problem
Detector saturation limits secret key rates for low-loss QKD channels.
Method
The system uses a prepare-and-measure protocol with decoy states, d = 4 time-bin quantum states, interferometric phase-state measurements, and a composable security definition.
Results
26.2 Mbits/s was achieved at 4 dB channel loss, equivalent to 20 km of optical fiber, reported as the highest secret key rate at that loss.
Takeaways & Limitations
Using more than one secret bit per received photon can essentially double the secret key rate of a d = 4 protocol at detector saturation compared with a qubit protocol.
Takeaways & Limitations
The lower probability of detection in the central time bin reduces the events used in security analysis and lowers the secret key rate.
Abstract
from arXiv · showhide
The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders-of-magnitude lower than current classical communication systems. In an effort towards a commercially viable QKD system with improved key generation rates, we developed a discrete-variable QKD system based on time-bin quantum photonic states that is capable of generating provably-secure cryptographic keys at megabit-per-second (Mbps) rates over metropolitan distances. We use high-dimensional quantum states that transmit more than one secret bit per received photon, alleviating detector saturation effects in the superconducting nanowire single-photon detectors (SNSPDs) employed in our system that feature very high detection efficiency (of over 70%) and low timing jitter (of less than 40 ps). Our system is constructed using commercial off-the-shelf components, and the adopted protocol can readily be extended to free-space quantum channels. The security analysis adopted to distill the keys ensures that the demonstrated protocol is robust against coherent attacks, finite-size effects, and a broad class of experimental imperfections identified in our system.
RESULTS
The system uses four-dimensional time-bin and conjugate phase states in a prepare-and-measure QKD protocol, with decoy states and finite-key security analysis. It achieves high secret-key rates over metropolitan-scale channel losses while accounting for detector-rate-dependent efficiency.
- Protocol and security: The prepare-and-measure protocol uses a practical decoy-state method to estimate received single-photon statistics and bounds extractable secret-key length from measured noise.Alice attenuates laser wavepackets to the single-photon level, while Bob measures time or phase and uses sifted arrival-time data.
- State preparation: Four-dimensional time-bin states and their Fourier-conjugate phase states form the QKD encoding and measurement bases.Temporal states occupy distinct 66-ps wavepackets within 400-ps time bins; phase states are mutually unbiased with respect to temporal states.
- Phase measurement: A cascaded interferometric tree maps each phase state to a corresponding detector through constructive interference in the central time bin.The interferometers require no active path-length stabilization, and only central-bin events are used in the security analysis.
- Measured performance: 26.2 Mbits/s is achieved at 4 dB channel loss, equivalent to 20 km of optical fiber, with temporal- and frequency-basis error rates of 4.5% and 4.8%.The paper reports this as the highest secret-key rate at that quantum channel loss and reports record-high rates up to 16.6 dB, equivalent to 83 km.
- Detector effects: Detector efficiency exceeds 70% at 16.6 dB loss, but decreases at lower loss as detection rates increase because of finite detector reset time.The experiment characterizes efficiency as a function of detection rate and incorporates it into the security analysis.
- Range boundary: The simulated secret-key rate drops rapidly beyond 18 dB, or 90 km, mainly because fixed-duration data collection increases finite-key statistical uncertainty at higher loss.Higher loss reduces Bob’s received data and increases uncertainty in the phase-error rate.
DISCUSSION
The discussion attributes the high rates to high-dimensional encoding, efficient detectors, low jitter and dark counts, and a high clock rate. It also identifies interferometer loss, larger dimensions, and multiplexing as routes for further improvement.
- Rate mechanisms: High-dimensional encoding extracts more bits per received photon at detector saturation, essentially doubling the secret-key rate of the d = 4 protocol relative to qubit protocols.This advantage is most relevant for low-loss channels where detector saturation limits the rate.
- Detector performance: Superconducting nanowire detectors provide high efficiency, short reset time, nearly constant jitter below 40 ps, and low dark counts of 100-200 counts/s.These detector properties support a nearly constant quantum bit error rate as channel loss varies.
- System timing: Matching the time-bin spacing to detector jitter enables operation at a 2.5 GHz system clock rate.The paper states that the bin duration is only somewhat larger than detector jitter.
- Deployment: The time-phase-state protocol is suited to free-space deployment because turbulence does not scatter one photonic state into another when the wavepacket duration substantially exceeds 10 ps.This statement specifies the condition under which the temporal encoding remains robust to optical turbulence.
- Future improvements: Further rate improvements could come from lower-loss monolithic interferometers, increasing d, and dense-wavelength multiplexing with multiple transmitters.Multiplexing could use the telecommunication C-band with one set of interferometers but would require many single-photon detectors.
MATERIALS AND METHODS
The protocol combines a composable security definition, finite-key analysis, and interferometric measurements of four-dimensional time-bin phase states. Its sifting retains central-bin events for security, while detector and wavepacket constraints trade detection efficiency against secure-key rate.
- Security proof: The protocol is ε-secure when secrecy and correctness parameters satisfy ϵsec + ϵcor ≤ ε, making it composable with larger cryptographic protocols.Correctness is typically set by the hash-code length used for error verification.
- Security proof: The security analysis bounds secret-key length using vacuum and single-photon detections, the single-photon phase-error bound, and the measured basis overlap.The overlap parameter is c := −log2 max_i,j |⟨f_i|t_j⟩|^2.
- Calibration: The experiment measured a lower bound of c = 1.89 for the prepared-and-measured state overlap, using the worst-case matrix element.Ideal four-dimensional mutually unbiased states would correspond to c = 2.
- Phase-state detection: Phase-state detection uses cascaded interferometers, with delays of 2τ in the first stage and one time bin in the second stage.The first-stage interferometer splits and recombines each phase-state wavepacket before the second-stage interference measurements.
- Phase-state detection: Interferometric outputs occupy seven time bins, but only central-bin events are used for security because they correspond one-to-one with incident phase states.There is a 75% chance of detection outside the central time bin in each channel; sifting prevents spill-over from increasing the error rate.
- Rate trade-offs: The lower central-bin detection probability reduces events entering the security analysis, while higher-dimensional protocols provide greater noise tolerance and can increase the secure rate.Figure 3a evaluates experimentally achievable secret-key rates against channel loss for N = 6.25 × 10^10 signals over a 100-s session.