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Quantum Simulation Entanglement Theory Quantum Correlations Quantum State Preparation Representation Quantum Entropy Information Measures

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

arXiv

Authors: Lu Wei

Year

2017

Paper ID

44995

Status

Preprint

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~2 min

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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 mleq n is given by \begin{equation*} -ψ_{1}\leftmn+1right+\frac{m+n}{mn+1}ψ_{1}\leftnright-\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \end{equation*} where ψ₁\(cdot\) is the trigamma function. We give a proof of this formula.

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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It was recently conjectured by Vivo, Pato, and Oshanin [Phys.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1706.08199 [2] arXiv https://arxiv.org/abs/1706.08199 [3] Publisher https://arxiv.org/abs/1706.08199

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