Detecting Consistency of Overlapping Quantum Marginals by Separability

TL;DR

This paper introduces a new method for checking the consistency of overlapping quantum marginals by analyzing the separability of derived states, offering insights into the quantum marginal problem and its relation to separability criteria.

Contribution

It proposes a novel approach to the quantum marginal problem using separability analysis, extending the understanding of $k$-symmetric extension and overlapping marginals.

Findings

Effective for $k$-symmetric extension problems

Applicable to some cases of overlapping marginal problems

Provides a converse perspective to existing separability criteria

Abstract

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability.