Finer Characterizations of Pure Bipartite Entanglement

TL;DR

This paper introduces a new necessary and sufficient criterion for pure bipartite state separability, providing finer measures of entanglement and clarifying the role of the Peres-Horodecki criterion in this context.

Contribution

It presents a novel criterion for pure bipartite entanglement, establishing its equivalence with the Peres-Horodecki criterion and detailing measures of maximal entanglement.

Findings

New criterion for pure bipartite separability

Peres-Horodecki criterion is necessary and sufficient for pure states

Detailed characterization of maximally entangled states

Abstract

A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability or non-separability determination) are discussed. Based on this criterion, we proved that the well-known Peres-Horodecki positivity-of-partial-transform criterion is also necessary and sufficient for separability in the case of pure bipartite systems. The maximum value of entanglement, and the corresponding maximally-entangled states are also worked out in detail.