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arXiv · 1706.08199

A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy

Lu Wei
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Abstract

It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\leq n$ is given by \begin{equation*} -ψ_{1}\left(mn+1\right)+\frac{m+n}{mn+1}ψ_{1}\left(n\right)-\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \end{equation*} where $ψ_{1}(\cdot)$ is the trigamma function. We give a proof of this formula.

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Lu Wei. 2017-07-11. A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy. https://doi.org/10.1103/physreve.96.022106

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