Enhanced Simultaneous Quantum-Classical Communications Under Composable Security

Simultaneous quantum-classical communications (SQCC) protocols are a family of continuous-variable quantum key distribution (CV-QKD) protocols which allow for quantum and classical symbols to be integrated concurrently on the same optical pulse and mode. In this work, we present a revised analysis of simultaneous quantum-classical communications in Gaussian-modulated coherent-state CV-QKD protocols. We address security concerns inherently associated with SQCC schemes and provide an updated model of the coupling between the classical and quantum channels. We provide evidence for our model via Monte Carlo simulation. We compute the performance of our revised SQCC protocol in terms of the secret-key generation rate optimised over free parameters and demonstrate improved quantum efficiency for a given classical bit-error rate. Lastly, we extend our analysis into the finite-key regime, where we propose a scheme for composably-secure SQCC under realistic operating conditions and demonstrate that our scheme retains the advantage in quantum performance over previous models.

💡 Research Summary

This paper presents a comprehensive enhancement of Simultaneous Quantum-Classical Communication (SQCC) protocols within the framework of Gaussian-modulated coherent-state Continuous-Variable Quantum Key Distribution (CV-QKD). SQCC protocols allow the concurrent transmission of classical data and quantum information on the same optical pulse, offering significant practical advantages for bandwidth-efficient network integration, such as in satellite communications.

The authors begin by identifying key limitations in prior SQCC models: an oversimplified description of the coupling between classical and quantum channels, a lack of explicit composable security analysis, and reliance on the unrealistic assumption of an infinitely long secret key. To address these issues, the paper proposes a revised SQCC protocol designed for composable security in the finite-key regime.

The core protocol combines a standard GMCS CV-QKD scheme with a classical Quadrature Phase-Shift Keying (QPSK) modulation. For security analysis, the authors employ an equivalent entanglement-based description. A crucial conceptual shift is made: the large classical displacement is modeled as occurring after the quantum signal passes through the untrusted channel and just before Bob’s measurement. This virtual protocol assumes Eve has perfect knowledge of the classical signal, which constrains her optimal attack to a Gaussian one (invoking Gaussian optimality) and simplifies the security proof by aligning with the realistic threat model where classical communication is not secure.

A major technical contribution is the accurate characterization of the quantum measurement statistics after Bob’s post-processing. The authors demonstrate analytically and via Monte Carlo simulation that Bob’s process of threshold discrimination (to identify the classical symbol) and subsequent re-displacement to recover the quantum signal does not simply result in a broadened Gaussian distribution, as previously assumed. Instead, it creates a non-Gaussian distortion of the statistics. Left uncorrected, this could lead to non-physical data and compromise security.

To close this security loophole, the paper introduces an essential renormalization step. After re-displacement, Bob scales his data by an electronic gain factor. This process “physicalizes” the output, ensuring the final measurement statistics are identical to those from a legitimate, purely Gaussian virtual protocol. Only after this renormalization can the principles of Gaussian extremality be safely applied to bound Eve’s accessible information (the Holevo quantity).

Using this secured model, the authors compute the secret-key generation rate. In the asymptotic regime (infinite key), they optimize over free parameters and demonstrate a clear improvement in quantum efficiency for a given classical bit-error rate compared to the previous leading SQCC model. Furthermore, they extend the analysis to the more practical finite-key regime. They propose a concrete scheme for composably-secure SQCC under realistic conditions and show that the performance advantage of their improved model is maintained even with finite key effects. This work significantly strengthens the security foundation of SQCC protocols and enhances their feasibility for real-world deployment where resources are constrained.