A counter-argument to "Hidden variable models for quantum theory cannot have any local part" arXiv:0801.2218

TL;DR

This paper challenges previous claims that local hidden variables in quantum models cannot have a local part, arguing that their assumptions are not universally valid and providing a counter-example to prior conclusions.

Contribution

It demonstrates that hidden variables are not observables and their probability distributions need not satisfy non-signaling, countering prior assumptions and conclusions.

Findings

Hidden variables are not observables.

Probability distributions of hidden variables may violate non-signaling.

Counter-example shows previous assumptions are not universally valid.

Abstract

Colbeck and Renner [arXiv:0801.2218] analyzed a class of combined models for entanglements in which local and non-local hidden variables cooperate for producing the measurement results. They came to the conclusion that the measurement results are fully independent of the local components of the hidden variables. Their conclusion is based mainly on an assumption on the local hidden variables, assumption similar to the non-signaling property of probabilities of observables' values. In the present text it is proved that hidden variables are not observables, so their distributions of probabilities do not necessarily possess the non-signaling property. Also, a counter-example is brought to the Colbeck and Renner assumption, showing that their type of models and conclusion are not general. The question whether hidden variables, local or non-local, exist or not, remains open.