Partial Transpose As A General Criterion for the Separability of Quantum States

TL;DR

This paper introduces a criterion based on partial transposition and symmetrization for determining the separability of quantum states of identical particles, showing that such states are always separable and linking it to realignment criteria.

Contribution

It extends separability criteria to identical particles using partial transposition and symmetrization, establishing their equivalence to realignment criteria and demonstrating all bipartite states of identical particles are separable.

Findings

Bipartite states of identical particles are always separable.

Partial transposition combined with symmetrization is effective for separability checks.

The criterion is equivalent to the realignment criterion.

Abstract

Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems (fermion systems) can be used to check whether a state is separable or not.By using determinant based separability criteria it has been found that bipartite states of identical particles are always separable. It is found that partial transposition and symmetrization is equivalent to realignment criteria proposed by Wu.