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Communications in computer and information science

Multi-level Parameter Estimation for Receiver Noise in CV-QKD

Guillaume Ricard, Yves Jaouën, Romain Alléaume

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-13852-1_16

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Near-optimal binary coherent state discrimination can be achieved by performing a displacement operation followed by photon detection. This displacement serves as a control parameter that can be tuned to optimize a chosen figure of merit, which makes such receivers attractive beyond state discrimination. Here, we turn this discrimination strategy into a complete continuous-variable quantum key distribution (CV-QKD) protocol based on a binary alphabet of noisy coherent states (displaced thermal states) and displacement receivers. We develop a strategy for estimating the channel parameters with the same displacement receiver, since standard quadrature-based methods do not apply. While a key map can be obtained with on/off detection, we demonstrate that reliable parameter estimation requires photon-number-resolving detection with sufficient resolution. Finite detector resolution underestimates the observed noise and constitutes a potential security loophole, which we quantify and show to be mitigable with modest resolution. We analyze the protocol's security against entangling-cloner collective attacks in the asymptotic regime, for both direct and reverse reconciliation, and show that it can generate secret keys even under noisy state preparation and imperfect detection. Interestingly, we find that the displacement that minimizes the discrimination error probability also performs well for key generation, thus providing a useful and analytically tractable tuning strategy for the CV-QKD receiver. We evaluate the protocol's performance over a range of transmittances and noise parameters, showing that the displacement receiver can outperform conventional homodyne detection in experimentally relevant regimes. Together, our results point to displacement receivers as a promising alternative for CV-QKD implementations.
Continuous-Variable Quantum Key Distribution (CV-QKD) is a form of quantum cryptography that encodes information in the amplitude and phase of light, enabling provably secure key sharing over optical channels. Building on previous research, subcarrier multiplexing configurations have been proposed to allow a quantum channel and a classical data channel to share a single optical carrier and transmitter. In these schemes, advanced Digital Signal Processing (DSP) enables the high Signal-to-Noise Ratio (SNR) classical signal to serve as a phase reference for the quantum channel, facilitating phase recovery without dedicated pilot tones. This thesis integrates these concepts into a complete system architecture that combines CV-QKD with One-Time Pad encrypted communication over a single fiber and transmitter, bringing practical implementation closer to a scenario where classical and quantum communication modes can be selected purely via software. A detailed link-budget analysis quantifies trade-offs between classical and quantum data rates and ensures sufficient bandwidth for essential post-processing tasks such as reverse reconciliation and parameter estimation.Beyond system integration and experimental improvements, this work rigorously addresses practical security. Three contributions enhance parameter estimation under realistic conditions. First, the Multi-Level Parameter Estimation scheme allows continuous receiver-noise calibration via an intensity modulator without interrupting key generation, significantly increasing throughput. Second, a DSP-induced mode mismatch is characterized: the receiver's digital filters and hardware response define the measured quantum mode, which may deviate from the sender's calibration and bias critical parameter estimation. Third, the Time-Gated Variance formalism quantifies calibrations in the presence of realistic non-white noise, accounting for the impact of calibration duration on variance estimation. Together, these methods provide a more accurate, quantitative foundation for assessing transmittance and excess noise, improving both security and performance.Although demonstrated on a single-fiber, subcarrier-multiplexed system, these techniques are broadly applicable to other CV-QKD architectures. By combining such system designs with rigorous, quantitative analysis of noise calibrations, this thesis takes a step toward scalable, certifiable quantum-secured communication, bridging the gap between theoretical security and real-world deployment.