Smooth Max-Information as One-Shot Generalization for Mutual Information
Smooth Max-Information as One-Shot Generalization for Mutual Information
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DOI：
10.1109/tit.2013.2295314
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发表时间：
2014-03-01
影响因子：
2.5
通讯作者：
Renner, Renato
中科院分区：
文献类型：
--
作者：
Ciganovic, Nikola;Beaudry, Normand J.;Renner, Renato
我们研究了光滑最大信息的形式性质，这是由最大相对熵导出的von Neumann互信息的一种推广。最近的研究表明，它在单次信道编码、量子速率失真理论和量子多体系统的物理学中是一个有用的量。最大信息可以用多种方式定义。我们证明了不同的平滑定义本质上是等效的（直到平滑参数中的对数项）。这些等价关系使我们能够从最小和最大熵的角度推导出最大信息的新的链式规则，从而将光滑熵的形式化扩展到互信息。
We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate distortion theory, and the physics of quantum many-body systems. Max-information can be defined in multiple ways. We demonstrate that different smoothed definitions are essentially equivalent (up to logarithmic terms in the smoothing parameters). These equivalence relations allow us to derive new chain rules for the max-information in terms of min- and max-entropies, thus extending the smooth entropy formalism to mutual information.