Enhanced Simultaneous Quantum-Classical Communications Under Composable Security

TL;DR

The paper develops an enhanced, composably secure SQCC framework for Gaussian-modulated CV-QKD, integrating classical coherent-state communication with quantum signals through a threshold-based postprocessing and a renormalisation step. By mapping to a virtual entanglement-based Gaussian protocol and leveraging Gaussian optimality, it derives a refined covariance description and validates it with large-scale Monte Carlo simulations. The results yield improved asymptotic and finite-key secret-key rates over prior SQCC models, showing a tangible quantum advantage at fixed classical QoS and enabling practical deployment considerations, including satellite scenarios. The work lays a rigorous foundation for hybrid quantum-classical communications, while acknowledging practical constraints and outlining avenues for further optimization and experimental realization.

Abstract

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.

Figures (5)

• Figure 1: Protocol diagram describing the secure SQCC scheme described in Section \ref{['sec:protocol_description']} in the prepare-and-measure picture (a), and the equivalent entanglement-based picture (b) used for security analysis. In the entanglement-based picture, Alice shares one mode of a two-mode squeezed vacuum state (TMSVS), which she passes through a noisy channel $\mathcal{E}(T,\varepsilon)$ before displacing it by some large displacement to encode a classical symbol. We model Alice's classical displacement as occurring after the outgoing TMSVS mode is passed through the channel to encode the assumption that Eve has perfect knowledge of the classical communications, and so can reconstruct Alice's original Gaussian state from the combined signal with perfect fidelity. This allows Alice and Bob to infer Eve's optimal attack, and consequently her information, via Gaussian optimality. Bob then measures the outgoing mode, emulates Alice's original quantum signal via threshold discrimination and re-displacement, and renormalises the data to produce a measurement distribution consistent with a Gaussian channel, from which Alice and Bob infer Eve's information and distill a shared secret key.
• Figure 2: Monte Carlo simulations of the joint measurement distribution possessed by Alice and Bob for $N = 10^8$ shots. (a) A simulated distribution of Bob's data $\tilde{\beta}$ immediately after heterodyne measurement of the joint quantum state described by Eqs. \ref{['eq:init_mean']}-\ref{['eq:init_covar']}, evaluated for Alice's modulation variance $V = 5$, channel transmissivity $T = 0.1$, channel excess noise $\varepsilon = 0.05$ and initial classical displacement $d = 12$. Each combined quantum and classical symbol sent by Alice manifests as a large displacement in the phase space in one of the four cardinal directions, encoding a classical bit string, together with a smaller quantum fluctuation encoding a quantum symbol. (b) Identifying each symbol's classical data via the threshold discrimination process and re-displacing accordingly causes the postprocessed measurements $\tilde{\beta}_d$ to assume a quasi-Gaussian distribution, with the degree of non-Gaussianity proportional to the overlap of the joint quantum-classical symbols. (c) A comparison of the covariance matrix elements $a_d$, $b_d$ and $c_d$ characterising Alice and Bob's joint postprocessed distribution, as predicted by theory (solid lines) and as calculated empirically via generation and postprocessing of $10^5$ simulated 'real' measurements (squares).
• Figure 3: Asymptotic keyrates of the improved SQCC protocol introduced in this work ($K^\infty$, solid lines) compared against the SQCC protocol described by qi_noise_2018 ($K^\infty_{[16]}$, dashed lines). We assume the untrusted excess noise of the channel is $\varepsilon = 0.05$ and the reconciliation efficiency of the protocol is $\beta = 0.95$. At each $T$, the classical displacement $d$ is chosen by Alice such that Bob's classical bit-error rate is fixed at $\mathcal{W}$ and the keyrate is optimised over Alice's modulation variance $V$.
• Figure 4: Finite-size secret-key fractions for the improved SQCC protocol ($K^\mathcal{F}$, solid lines). The secret-key fraction is calculated from initial block size $N = 10^8$ under the same protocol parameters and optimization as in Fig. \ref{['fig:pubfig_asymptotic']}. Further finite-size security parameters are detailed in Appendix \ref{['app:fnsz_keyrate']}, Table \ref{['tab:security_params']}.
• Figure 5: The physical protocol (top) and equivalent virtual protocol (bottom) of the SQCC scheme. For an inferred keyrate to be a valid lower bound on the distillable secret information, the effective virtual channel $\mathcal{\hat{P}}$ that emulates the postprocessing and rescaling must be identifiable with a physically legitimate operation.