Witnessing quantum discord in 2 x N systems

TL;DR

This paper demonstrates that in 2 x N quantum systems, the positivity of partial transposition with respect to a canonical factorization serves as a witness for quantum discord, extending the understanding of quantum correlations beyond entanglement.

Contribution

It introduces the concept of SPPT states in 2 x N systems and establishes a new criterion to detect quantum discord based on partial transposition properties.

Findings

SPPT states are a subset of PPT states with a specific positivity property.

Non-SPPT states in 2 x N systems necessarily have nonclassical correlations.

The criterion parallels the Peres-Horodecki criterion for entanglement detection.

Abstract

Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show that 2 x N states satisfy additional property: the positivity of their partial transposition is recognized with respect to the canonical factorization of the original density operator. We call such states SPPT (for strong PPT). Therefore, we provide a natural witness for a quantum discord: if a 2 x N state is not SPPT it must contain nonclassical correlations measured by quantum discord. It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.