Entropy in general physical theories
Entropy in general physical theories
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DOI：
10.1088/1367-2630/12/3/033023
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发表时间：
2009-09
影响因子：
3.3
通讯作者：
A. J. Short;S. Wehner
中科院分区：
文献类型：
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作者：
A. J. Short;S. Wehner
信息在我们理解物理世界中起着重要作用。因此，我们提出了一个熵的信息测量的任何物理理论，承认系统，状态和测量。在量子和经典世界中，我们的测量分别减少到冯诺依曼和香农熵。它甚至可以用在量子或经典环境中，在那里我们只允许执行有限的一组操作。在一个以非局部盒子形式存在超强相关性的世界中，我们的测量可以用来分析诸如超强随机访问编码和违反“信息能力”等协议。然而，我们也表明，在这样一个世界中，没有熵的措施可以表现出所有的属性，我们通常接受的量子设置。例如，不存在条件熵的“合理”度量是次加性的。最后，我们证明了一个编码定理的一些理论，是类似于量子和经典的设置，为我们提供了一个有吸引力的操作解释。
Information plays an important role in our understanding of the physical world. Hence we propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical worlds, our measure reduces to the von Neumann and Shannon entropies, respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of ‘information causality’. However, we also show that in such a world no entropic measure can exhibit all the properties we commonly accept in a quantum setting. For example, there exists no ‘reasonable’ measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical settings, providing us with an appealing operational interpretation.