关于随机纯态中Tsallis纠缠熵的精确方差
On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State.
作者信息
Wei Lu
机构信息
Department of Electrical and Computer Engineering, University of Michigan, Dearborn, MI 48128, USA.
出版信息
Entropy (Basel). 2019 May 27;21(5):539. doi: 10.3390/e21050539.
The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.
Tsallis熵是量子信息理论中对标准冯·诺依曼熵的一种有用的单参数推广。在这项工作中，我们研究了处于随机纯态的二分量子系统的Tsallis熵的方差。主要结果是一个Tsallis熵的精确方差公式，它涉及一些终止超几何函数的有限和。在二次熵和小子系统维度的特殊情况下，主要结果进一步简化为显式方差表达式。作为一个副产品，我们基于导出的与Tsallis熵的矩关系，找到了最近证明的冯·诺依曼熵方差公式的一个独立证明。
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