Seminar Event Detail


Integrable Systems and Random Matrix Theory

Date:  Monday, October 30, 2017
Location:  1866 East Hall (4:00 PM to 5:00 PM)

Title:  On the exact moments of von Neumann entropy of quantum bipartite systems

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)},<br
\end{equation*}
where $\psi_{1}(\cdot)$ is the trigamma function. We give a proof of the above formula in this talk. We also discuss some possible approaches to obtain the exact higher moments.

Files:


Speaker:  Lu Wei
Institution:  University of Michigan-Dearborn

Event Organizer:   Thomas Bothner    bothner@umich.edu

 

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