Emergent Mind
A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
(1706.08199)
Published Jun 26, 2017
in
math-ph
,
cs.IT
,
math.IT
,
math.MP
,
and
quant-ph
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} -\psi{1}\left(mn+1\right)+\frac{m+n}{mn+1}\psi{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.
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