Quantum states with strong positive partial transpose

TL;DR

This paper introduces a new class of bipartite quantum states called states with strong positive partial transpose (SPPT), which are PPT by construction, and conjectures that all SPPT states are separable.

Contribution

The paper defines the class of SPPT states, explores their properties, and conjectures their separability, expanding understanding of PPT states in quantum information.

Findings

SPPT states are a proper subset of PPT states.

All SPPT states are conjectured to be separable.

The class is constructed via canonical factorization of density operators.

Abstract

We construct a large class of bipartite M x N quantum states which defines a proper subset of states with positive partial transposes (PPT). Any state from this class is PPT but the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator. We propose to call elements from this class states with strong positive partial transposes (SPPT). We conjecture that all SPPT states are separable.