Second-order statistics of fermionic Gaussian states

TL;DR

This paper derives explicit formulas for the second-order statistics of entanglement in fermionic Gaussian states, revealing insights into entropy fluctuations and entanglement capacity growth.

Contribution

It provides the first exact formulas for the variance of von Neumann entropy and mean entanglement capacity in fermionic Gaussian states, including a conjecture for the general variance.

Findings

Exact formulas for second-order statistics of entanglement

Analytical evidence for Gaussianity of von Neumann entropy

Linear growth of average entanglement capacity

Abstract

We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy and entanglement capacity. The focus is on the variance of von Neumann entropy and the mean entanglement capacity that belong to the so-defined second-order statistics. The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences. We also conjecture the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions. Based on the obtained results, we analytically study the numerically observed phenomena of Gaussianity of von Neumann entropy and linear growth of average capacity.