Smallest state spaces for which bipartite entangled quantum states are separable

TL;DR

This paper investigates the minimal local operator sets needed to render bipartite entangled states separable, offering new insights into classical models and quantum measurement restrictions.

Contribution

It identifies the smallest local operator sets that make pure bipartite entangled states appear separable, including for maximally entangled states, expanding understanding of quantum-classical boundaries.

Findings

Many inequivalent solutions for maximally entangled states

Phase point operators relate to discrete Wigner functions

Provides alternative methods for local hidden variable models

Abstract

According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only restricted set of measurements are available. With such motivations in mind, we ask what are the smallest such sets of local operators such that a pure bipartite entangled quantum state becomes separable? We find that in the case of maximally entangled states there are many inequivalent solutions, including for example the sets of phase point operators that arise in the study of discrete Wigner functions. We therefore provide a new way of interpreting these operators, and more generally, provide an alternative method for constructing local hidden variable models for entangled quantum states under subsets of quantum measurements.