Average capacity of quantum entanglement

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.

arXiv comment21 pages, 1 figure

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• Average relative entropy of random states
• Entanglement capacity of fermionic Gaussian states
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Average mutual information for random fermionic Gaussian quantum states