Bipartite entanglement in systems of identical particles: the partial transposition criterion

TL;DR

This paper investigates bipartite entanglement in systems of identical bosons, establishing conditions under which partial transposition accurately detects entanglement using a generalized separability concept.

Contribution

It introduces a generalized separability definition for identical particles and identifies states where partial transposition is both necessary and sufficient for entanglement detection.

Findings

Partial transposition is a reliable entanglement criterion for certain bosonic states.

A generalized separability concept is developed for systems without tensor product structure.

Classification of states where partial transposition fully detects entanglement.

Abstract

We study bipartite entanglement in systems of N identical bosons distributed in M different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given in terms of commuting subalgebras of observables. Using this generalized notion of separability, we classify the states for which partial transposition turns out to be a necessary and sufficient condition for entanglement detection.