具有互保密的量子广播信道

中文摘要 AI 辅助

我们研究了在量子广播信道上传输两个独立的保密经典消息，每个接收者各接收一个消息。每个消息必须对其他接收者保密，包括当该接收者已知自己的消息时。对于经典输入和量子输出，我们在平均可靠性和条件强保密性下建立了经典的Marton型内界。编码器使用归一化似然权重从独立生成的码本中选择码字对。我们通过分布变化论证证明了可靠性。我们的主要技术结果是二分经典-量子可分辨性定理，该定理考虑了由码字对选择产生的依赖性，并为同一编码器建立了保密性。我们还获得了多字母容量表征，并将其扩展到在针对其他接收者及其Stinespring环境的保密性下的任意量子输入。我们恢复了确定性经典和退化经典-量子信道的保密容量区域，并对经典Blackwell信道进行了显式评估。对于单射确定性经典广播信道的相干等距扩展，我们证明了保密经典容量区域等于相应经典信道的容量区域。然后，我们将保密经典通信与量子传输进行比较。对于Blackwell信道的相干等距扩展，我们确定了无辅助量子容量区域，并表明一些可实现的保密经典速率对位于该区域之外。Platypus信道提供了这种分离的另一个例子。

英文摘要

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.

发表机构

• Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）
• Department of Combinatorics and Optimization, University of Waterloo（滑铁卢大学组合数学与优化系）
• Department of Applied Mathematics, University of Waterloo（滑铁卢大学应用数学系）
• Perimeter Institute for Theoretical Physics（理论物理珀蒂默研究所）
• Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）

机构由 AI 辅助整理，请以论文原文为准。