Application of $\alpha$-order Information Metrics for Secure Communication in Quantum Physical Layer Design

TL;DR

This paper explores the use of $lpha$-order Re9nyi entropy metrics to enhance secure quantum communication, addressing practical non-asymptotic scenarios and revealing trade-offs between reliability and security.

Contribution

It introduces a framework using $lpha$-order Re9nyi entropy for non-asymptotic security analysis in quantum physical layers, applied to BPSK over lossy channels.

Findings

Current coding rates may not support positive secure rates.

Higher coding rates or longer frames are needed for better security.

The framework demonstrates the utility of $lpha$-order measures in quantum security.

Abstract

Quantum physical layer security protocols offer significant advantages, particularly in space communications, but their achievable secrecy rates are often limited to the asymptotic regime. Realistic communication systems, however, demand non-asymptotic solutions. Recently, the $\alpha$-order information-theoretic metrics based on R\'enyi entropy has been proposed. We study their practical applicability to engineering secure quantum communication systems. By deriving a composable security bound using sandwiched R\'{e}nyi entropy, we apply our framework to a practical scenario involving BPSK modulation over a lossy bosonic channel, consistent with DVB-S2X standards. We highlight a critical trade-off between reliability and security, by showing that current coding rates may fall short of supporting positive secure coding rates under physical layer security considerations. This emphasizes the need for higher coding rates or additional frame lengths to balance reliability-security trade-offs effectively. Through this application, we demonstrate the utility of $\alpha$-order measures for advancing secure communication in quantum physical layer designs.