Software-enhanced simultaneous quantum-classical communication protocol with Gaussian post-selection

Simultaneous quantum-classical communication (SQCC) protocols offer a practical approach to continuous-variable quantum key distribution (CV-QKD) by encoding quantum and classical signals onto the same optical pulse. However, like most QKD protocols, their performance is limited when experimental parameters, such as modulation variance, are optimised based on stationary channel assumptions. In fluctuating environments, such as free-space links, this can result in sub-optimal key rates and reduced transmission distances. In this work, we introduce Gaussian post-selection into the SQCC framework, enabling a software-based optimisation of the modulation variance after channel estimation. This passive approach enhances key rates in both asymptotic and finite-size regimes without requiring hardware modifications and remains effective even when receiver imperfections are taken into account. We demonstrate that our protocol improves the transmission distance and robustness of SQCC relative to the standard fixed-variance SQCC protocol, and approaches the performance of a fully pre-optimised system across both fibre and free-space channels. In particular, we show that the protocol enables full communication windows under ideal weather conditions and maintains higher duty cycles during adverse weather in satellite-to-ground scenarios. These results highlight the practicality of post-selection based SQCC for real-world quantum communication over both terrestrial fibre networks and satellite-based free-space links.

💡 Research Summary

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The paper addresses a critical limitation of simultaneous quantum‑classical communication (SQCC) protocols: the reliance on a pre‑optimised modulation variance that assumes stationary channel conditions. In realistic scenarios such as free‑space or satellite‑to‑ground links, channel loss and excess noise fluctuate rapidly, making a fixed variance sub‑optimal or even unusable. To overcome this, the authors introduce a software‑only Gaussian post‑selection (GPS) technique into the SQCC framework, allowing the modulation variance to be effectively re‑optimised after channel estimation without any hardware modifications.

The protocol builds on the SQCC scheme of Zaunders et al. (2022). Alice prepares coherent states whose quadratures are drawn from a bivariate Gaussian distribution with variance (V_{\text{mod}}). She then adds a large classical displacement chosen from a discrete alphabet. After transmission through a thermal‑loss channel (characterised by transmittance (T) and excess noise (\xi)), Bob performs heterodyne detection, applies the inverse displacement, and rescales his data with an electronic gain (N_d) to restore a physical Gaussian distribution that may have been distorted by imperfect re‑displacement.

After the usual parameter estimation, if the estimated channel indicates that the original modulation variance is not optimal, Alice applies a Gaussian filter
(F_A(x,p)=\exp