On the separability of unitarily invariant random quantum states - the unbalanced regime

TL;DR

This paper investigates the entanglement properties of large unitarily invariant random quantum states, especially in the unbalanced regime where one subsystem size remains fixed while the other grows, linking spectral distribution to entanglement criteria.

Contribution

It provides new characterizations of entanglement and PPT properties of unitarily invariant states based on their spectral distribution in the unbalanced asymptotic regime.

Findings

Spectral distribution determines entanglement properties.

Characterization of PPT property via spectral data.

Asymptotic analysis in unbalanced regimes.

Abstract

We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.