On the joint distribution of the marginals of multipartite random quantum states

TL;DR

This paper analyzes the joint distribution of marginals of random Wishart matrices in multipartite quantum systems, revealing asymptotic freeness and connecting matrix integrals with combinatorial maps, with applications in quantum information.

Contribution

It introduces a combinatorial framework for studying marginals of random quantum states and establishes their asymptotic freeness in the balanced regime.

Findings

Marginals are asymptotically free in the balanced asymptotic regime.

Develops combinatorial machinery linking matrix integrals and maps.

Provides applications to random quantum states in quantum information.

Abstract

We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.