Hidden variable models for entanglements can or cannot have a local component?

TL;DR

This paper examines whether local hidden variables can influence entanglement models, extending previous work by analyzing less restrictive models and demonstrating that local components generally do not affect measurement outcomes, but alternative models may include local influences.

Contribution

It broadens the analysis of hidden variable models for entanglement by relaxing previous constraints and introduces a new class allowing local hidden variables alongside non-local influences.

Findings

Local hidden variables have no effect in the studied models.

A new class of models admits local hidden variables with non-local influences.

Previous restrictive proofs are extended to more general cases.

Abstract

A recent article of Colbeck and Renner tackled the problem whether entanglements may be explained by combined models of local and non-local hidden variables. To the difference from previous works they considered models in which each pair of entangled particles behaves in the same way, and the particles in the pair are equivalent, i.e. each of them produces its response to a measurement according to both local and non-local hidden variables. Their article aimed at proving that the local hidden variable component in such models has no effect on the measurement results, i.e. only the non-local variables are relevant. However, their proof deals with a very restrictive case and assumes questionable constraints on the hidden variables. The present text studies the Colbeck and Renner class of models on a less restrictive case and under no constraints on the hidden variables. It is shown again that the local component cannot have any influence on the results. However, the Colbeck and Renner class of models is not the only one possible. A different class is described, and it admits local hidden variables by the side of the non-local influence. This class presents a couple of advantages.