Separability of Multi-Partite Quantum States

TL;DR

This paper introduces a tensor decomposition method for density matrices to analyze the separability of multi-partite quantum states, providing criteria and bounds for determining when states are separable.

Contribution

It presents a novel tensor decomposition approach for density matrices and extends separability criteria to multi-partite states with new bounds based on spectral properties.

Findings

Separable indicator is non-negative if and only if the state is separable.

Derived bounds for the separable indicator using the spectrum of tensor factors.

Provided a practical criterion for separability in multi-partite quantum systems.

Abstract

We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands.