Entanglement capacity of fermionic Gaussian states

TL;DR

This paper investigates the entanglement capacity of fermionic Gaussian states, providing exact and asymptotic formulas for average capacity with and without particle number constraints, advancing understanding of quantum entanglement measures.

Contribution

It introduces new formulas for entanglement capacity of fermionic Gaussian states, generalizing previous results and developing novel tools for summation simplification.

Findings

Derived exact formulas for average capacity with particle number constraints

Established asymptotic formulas for capacity without constraints

Developed new mathematical tools for summation simplification

Abstract

We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic formulas of average capacity of two different cases - with and without particle number constraints. For the later case, the obtained formulas generalize some partial results of average capacity in the literature. The key ingredient in deriving the results is a set of new tools for simplifying finite summations developed very recently in the study of entanglement entropy of fermionic Gaussian states.