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Open AccessArticle

On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State

Department of Electrical and Computer Engineering, University of Michigan, Dearborn, MI 48128, USA
Entropy 2019, 21(5), 539; https://doi.org/10.3390/e21050539
Received: 26 April 2019 / Revised: 15 May 2019 / Accepted: 25 May 2019 / Published: 27 May 2019
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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. View Full-Text
Keywords: entanglement entropy; quantum information theory; random matrix theory; variance entanglement entropy; quantum information theory; random matrix theory; variance
MDPI and ACS Style

Wei, L. On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State. Entropy 2019, 21, 539.

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