On separable decompositions of quantum states with strong positive partial transposes

TL;DR

This paper introduces strong PPT (SPPT) states, a basis-dependent class of quantum states with positive partial transposes, and identifies a subset that are separable with explicit decompositions.

Contribution

It defines the class of strong PPT states and demonstrates that some are separable, providing explicit decompositions, advancing understanding of PPT state structures.

Findings

Existence of strong PPT states with basis-dependent positivity

Identification of a subset of SPPT states that are separable

Provision of explicit separable decompositions for these states

Abstract

We analyze a class of positive partial transpose states (PPT) such that the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator (Cholesky block decomposition). We call such PPT states strong PPT states (SPPT). This property, contrary to PPT, is basis dependent. It is shown that there exists a proper subset of SPPT states which are separable and provide a separable decomposition for any of these states.