Algorithmic construction of local hidden variable models for entangled quantum states

TL;DR

This paper introduces a straightforward method to construct local hidden variable models for entangled quantum states by verifying locality over finite measurement sets, enabling the identification of states with such models.

Contribution

The authors develop a simple, scalable approach to build LHV models for general entangled states, advancing the understanding of quantum nonlocality.

Findings

Method successfully constructs LHV models for various entangled states.

Sequence of tests fully characterizes states admitting LHV models in the limit.

Practical examples demonstrate the method's effectiveness.

Abstract

Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to general entangled states, which consists in verifying that the statistics resulting from a finite set of measurements is local, a much simpler problem. This leads to a sequence of tests which, in the limit, fully capture the set of quantum states admitting a LHV model. Similar methods are developed for constructing local hidden state models. We illustrate the practical relevance of these methods with several examples, and discuss further applications.