Local hidden--variable models for entangled quantum states

TL;DR

This paper reviews the development of local hidden-variable models for entangled quantum states over 25 years, highlighting cases where entanglement does not imply Bell inequality violations and discussing open questions.

Contribution

It provides a comprehensive overview of local hidden-variable models for entangled states, including bipartite and multipartite cases, and discusses key open problems in the field.

Findings

Some entangled states admit local hidden-variable models

Not all entangled states violate Bell inequalities

The review covers 25 years of research since Werner's work

Abstract

While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and, therefore, do not violate any Bell inequality. We provide an up to date overview of the existing local hidden--variable models for entangled quantum states, both in the bipartite and multipartite case, and discuss some of the most relevant open questions in this context. Our review covers twenty five years of this line of research since the seminal work by Werner [R. F. Werner, Phys. Rev. A 40, 8 (1989)] providing the first example of an entangled state with a local model, which in turn appeared twenty five years after the seminal work by Bell [J. S. Bell, Physics 1, 195 (1964)], about the impossibility of recovering the predictions of quantum mechanics using a local hidden--variables theory.