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

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 $m\le n$ 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 ${\psi }_1(\cdot )$ is the trigamma function. We give a proof of this formula.

Accepted for publication in Physical Review E

References in corpus (1)

• Statistical distribution of quantum entanglement for a random bipartite state

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