The quantum separability problem is a simultaneous hollowisation matrix analysis problem

TL;DR

This paper reformulates the quantum separability problem as a matrix analysis challenge, specifically determining if certain symmetric matrices can be simultaneously transformed into hollow matrices with zero diagonals.

Contribution

It extends the preconcurrence matrix formalism to multipartite systems, linking quantum separability to simultaneous hollowisation matrix analysis.

Findings

Separable states correspond to matrices unitarily congruent to hollow matrices.

Provides a new matrix-based criterion for multipartite separability.

Bridges quantum information theory with matrix analysis techniques.

Abstract

We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be formulated equivalently as a pure matrix analysis problem that consists in determining whether a given set of symmetric matrices is simultaneously unitarily congruent to hollow matrices, i.e., to matrices whose main diagonal is only composed of zeroes.