Average capacity of quantum entanglement

TL;DR

This paper investigates the average capacity of quantum entanglement as a measure for bipartite systems, deriving formulas for random states and demonstrating its effectiveness through numerical analysis.

Contribution

It provides exact and asymptotic formulas for the average entanglement capacity in major random state ensembles, extending previous partial results.

Findings

Derived formulas for Hilbert-Schmidt and Bures-Hall ensembles

Generalized previous results on average capacity

Numerical validation of capacity as an entanglement indicator

Abstract

As an alternative to entanglement entropies, the capacity of entanglement becomes a promising candidate to probe and estimate the degree of entanglement of quantum bipartite systems. In this work, we study the typical behavior of entanglement capacity over major models of random states. In particular, the exact and asymptotic formulas of average capacity have been derived under the Hilbert-Schmidt and Bures-Hall ensembles. The obtained formulas generalize some partial results of average capacity computed recently in the literature. As a key ingredient in deriving the results, we make use of recent advances in random matrix theory pertaining to the underlying orthogonal polynomials and special functions. Numerical study has been performed to illustrate the usefulness of average capacity as an entanglement indicator.