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Channel Simulation and Coded Source Compression

机译：通道仿真和编码源压缩

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摘要

Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This letter treats and solves the corresponding quantum coded source compression through an observation that connects coded source compression with channel simulation. First, we consider classical source coding with quantum side information, where the quantum side information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct coding theorem of our result is proved via the measurement compression theory of Winter, a quantum-to-classical channel simulation. Our result reveals that a helper's scheme which separately conducts a measurement and a compression is suboptimal, and measurement compression seems necessary to achieve the optimal rate region. We then study coded source compression in the fully quantum regime, where two different scenarios are considered depending on the types of communication channels between the legitimate source and the receiver. We further allow entanglement assistance from the quantum helper in both scenarios. We characterize the involved quantum resources and derive single-letter expressions of the achievable rate region. The direct coding proofs are based on well-known quantum protocols, the quantum state merging protocol, and the fully quantum Slepian-Wolf protocol, together with the quantum reverse Shannon theorem.
机译：编码源压缩（也称为带辅助源压缩）已成为分布式源压缩的主要变体，但迄今为止在量子方式中很少受到关注。这封信通过将编码源压缩与通道仿真联系起来的观察来处理和解决相应的量子编码源压缩。首先，我们考虑具有量子辅助信息的经典源编码，其中，辅助助手会观察量子辅助信息，并通过经典通道将其发送给解码器。我们得出此问题可达到的速率区域的单字母特征。我们的结果的直接编码定理是通过Winter的测量压缩理论，量子到经典信道模拟证明的。我们的结果表明，分别进行测量和压缩的辅助方案不是最佳的，并且测量压缩似乎对于实现最佳速率区域是必要的。然后，我们研究全量子状态下的编码源压缩，其中根据合法源与接收器之间的通信通道类型，考虑了两种不同的方案。在这两种情况下，我们还允许量子助手提供纠缠帮助。我们表征了涉及的量子资源，并得出了可达到的速率区域的单字母表达式。直接编码证明基于众所周知的量子协议，量子状态合并协议，完全量子Slepian-Wolf协议以及量子逆Shannon定理。

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