Quantum Broadcast Channels with Mutually Confidential Messages

2026-09-22

AI Summary

研究通过量子广播信道传输两个独立保密经典消息的问题，采用Marton型内界方法和归一化似然权重编码，确保消息对另一接收者保密。

Abstract

We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.

Problem

• quantum broadcast channel
• confidential messages
• mutual secrecy
• classical-quantum resolvability

Innovation

• quantum broadcast channel
• confidential classical messages
• bipartite classical-quantum resolvability theorem
• normalized likelihood weights
• secrecy