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High-Rate Continuous Variable Quantum Key Distribution Based on Probabilistically Shaped 64 and 256-QAM
François Roumestan, Amirhossein Ghazisaeidi, Jérémie Renaudier, Luis Trigo Vidarte, Eleni Diamanti, Philippe Grangier
TL;DR
This work addresses the challenge of obtaining high secret-key rates with discrete CV-QKD modulation while using practical commercial equipment. It combines probabilistically shaped QAM with an analytical security proof and reports average rates of 67.6 Mb/s for 64-QAM and 66.8 Mb/s for 256-QAM over 9.5 km of SMF.
Problem
Low-cardinality discrete modulation simplifies implementation and post-processing but reduces provable secret-key rates because its constellations poorly approximate a bidimensional Gaussian source.
Source: Introduction · p. 1Method
The system uses PCS QAM, an analytical security proof for arbitrary modulations adapted to a realistic receiver model, and worst-case excess-noise estimation.
Source: Modulation and security · p. 2Results
67.6 Mb/s with PCS 64-QAM and 66.8 Mb/s with PCS 256-QAM were achieved on average over 9.5 km of SMF, accounting for finite-size effects.
Source: Conclusion · p. 3Takeaways & Limitations
The results demonstrate the feasibility of CV-QKD using commercial components, standard DSP, and low-cardinality discrete constellations.
Source: Conclusion · p. 3The authors identify larger block sizes and improved overall experimental stability as possible ways to improve the results.
Source: Conclusion · p. 3
Abstract
from arXiv · showhide
We designed a CV-QKD system with off-the-shelf components and established the feasibility of distributing 67.6 and 66.8 Mb/s secret key rates on average over a 9.5 km SMF link, using respectively probabilistically shaped 64 and 256 QAM, and relying on a novel analytical security proof.
Introduction
CV-QKD is presented as a practical secure-communications approach compatible with commercial equipment, while low-cardinality modulation reduces provable key rates because its constellations poorly approximate a Gaussian source. This work applies a newer security proof to lower-cardinality QAM and reports higher secret-key rates than the authors’ previous demonstration.
Introduction
- 67.6 Mb/s with PCS 64-QAM and 66.8 Mb/s with PCS 256-QAM were averaged over 200 blocks on 9.5 km of SMF, accounting for finite-size effects.The work uses lower-cardinality formats and a higher symbol rate than the authors’ previous demonstration.Source: Introduction · p. 1
- Low-cardinality formats such as QPSK simplify implementation and post-processing but reduce provable secret-key rates because their constellations poorly approximate a bidimensional Gaussian source.Source: Introduction · p. 1
- The authors use a recently proposed proof establishing asymptotic security for discrete constellations of arbitrary cardinality to demonstrate lower-cardinality 64-QAM and 256-QAM.Source: Introduction · p. 1
Continuous Variable QKD
Alice sends randomly selected coherent states through an optical link, and Bob measures them using phase-diversity coherent detection. They estimate channel parameters, reconcile their data, and apply privacy amplification to obtain a final secret key.
Continuous Variable QKD
- Alice and Bob reveal part of their data to estimate channel parameters, correct transmission errors through reconciliation, and apply privacy amplification to produce the final key.Source: Continuous Variable QKD · p. 1
- The channel characterization defines Bob’s measured-state variance, Alice’s modulation variance, receiver efficiency, transmittance, electronic noise, and Bob-side excess noise in shot-noise units.The text identifies channel-entrance excess noise as ξA = 2ξB/(ηT).Source: Continuous Variable QKD · p. 1
- The section includes a PCS 64-QAM and 256-QAM symbol-probability histogram, an experimental testbed and DSP overview, and secret fraction versus VA under specified channel and receiver conditions.Source: Figure 1 · p. 1, Figure 2 · p. 2, Figure 3 · p. 2
Modulation and security
The system uses probabilistically shaped QAM and an analytical security approach adapted to realistic receiver noise and finite-sample parameter estimation. The modeled 256-QAM secret fraction is close to Gaussian modulation at its peak and exceeds that of 64-QAM.
Modulation and security
- PCS QAM assigns constellation points a Maxwell-Boltzmann distribution controlled by ν, optimized at each VA to minimize trace distance from Gaussian-modulated quantum states.The resulting discrete modulation has a Gaussianlike probability mass function over the square QAM lattice.Source: Modulation and security · p. 2
- The security analysis combines arbitrary-modulation asymptotic bounds with a realistic receiver model and uses a worst-case excess-noise estimator for finite-sample parameter estimation.The stated setting uses N = 2.8 × 10^6 symbols and security parameter ε = 10^-8.Source: Modulation and security · p. 2
- At its peak, 256-QAM has a secret fraction very close to Gaussian modulation and higher than 64-QAM.The inferred optimal VA values are around 5 for 64-QAM and 10 for 256-QAM.Source: Modulation and security · p. 2
Experimental system
The experiment uses off-the-shelf telecom components to transmit and detect a dual-polarization signal over a 9.5 km conventional singlemode-fiber link. The sampled waveforms are retained for offline digital signal processing.
Experimental system
- The setup uses a 9.5 km conventional SMF link with 2.2 dB characterized channel loss and a 600 MBaud dual-polarization signal.Source: Experimental system · p. 2
- A 5 GSample/s arbitrary waveform generator drives a dual-polarization I/Q optical modulator, while Bob detects the signal with a 180° hybrid and four amplified balanced photodiodes.Source: Experimental system · p. 2
- A 1 GHz oscilloscope samples the received waveforms at 5 GSample/s for offline DSP, and shot noise is periodically calibrated using an optical switch.Source: Experimental system · p. 2
Digital Signal Processing
The system interleaves QKD symbols with public QPSK pilots and uses standard optical DSP algorithms for signal recovery. Figure 4 tracks excess noise and secret key rate over time, and secret fraction over distance.
Digital Signal Processing
- QKD symbols are interleaved with deterministic QPSK pilots whose power is 14 dB higher than the QKD signal.The pilots are public information shared by Alice and Bob.Source: Digital Signal Processing · pp. 2–3
- Figure 4 plots Bob’s excess noise and secret key rate over time, plus secret fraction versus distance for PCS 64-QAM and PCS 256-QAM.The time-series measurements use a 9.5 km SMF link; the key-rate panel includes finite-size effects and uses β=0.95.Source: Figure 4 · p. 3
- Standard DSP uses matched filtering, pilot synchronization, polarization demultiplexing, carrier-frequency estimation, and pilot-aided carrier-phase estimation.The polarization-demultiplexing coefficients are updated on the pilots.Source: Digital Signal Processing · p. 3
Results
With the available commercial components and DSP, experimental PCS 64-QAM slightly outperforms PCS 256-QAM in secret key rate, despite the idealized advantage of 256-QAM at constant excess noise. The measurements average blocks over a 9.5 km SMF link.
Results
- The excess-noise and key-rate measurements cover 200 blocks over a two-hour experiment across 9.5 km SMF, using 2.8 × 10^6 symbols per variance estimate.Secret key rates use a worst-case estimator and reconciliation efficiency β=0.95.Source: Results · p. 3
- The secret-key-rate expression uses symbol rate, pilot rate, Alice–Bob mutual information, and Eve–Bob Holevo information, while the table summarizes measured averages.The symbol rate is 600 MBaud and the pilot rate is 1/2; the factor of 2 comes from polarization multiplexing.Source: Results · p. 3, Table 1 · p. 3
- At constant excess noise, ideal hardware and DSP favor 256-QAM, but experimentally 64-QAM has slightly better SKR and may reach up to 22 km.The reported experimental advantage is attributed to lower excess noise for 64-QAM with the available commercial components and DSP suite.Source: Results · p. 3
Conclusion
The work establishes feasible secret key distribution using PCS QAM over a 9.5 km SMF link with finite-size effects and an analytical security proof. It reports average rates of 67.6 Mb/s for PCS 64-QAM and 66.8 Mb/s for PCS 256-QAM.
Conclusion
- 67.6 Mb/s with PCS 64-QAM and 66.8 Mb/s with PCS 256-QAM were achieved on average over 9.5 km SMF with finite-size effects.The rates use a worst-case estimator and security parameter ε=10^-8.Source: Conclusion · p. 3
- The security analysis uses an analytical proof for arbitrary modulations to investigate PCS QAM in CV-QKD.Source: Conclusion · p. 3
- The authors identify larger block sizes and improved overall experimental stability as possible routes to better results.They frame the result as contributing to CV-QKD technology readiness using commercial components, standard DSP, and low-cardinality discrete constellations.Source: Conclusion · p. 3