Measurement dependence in a Bell inequality arising from the dynamics of hidden variables

TL;DR

This paper investigates how the dynamics of hidden variables during measurement can influence Bell inequalities by relaxing the assumption of measurement independence, revealing models that can induce measurement dependence.

Contribution

It introduces models of hidden variable dynamics during measurement, showing how measurement dependence can arise from the interaction with the environment.

Findings

Hidden variable dynamics can create measurement dependence.

Certain models can alter Bell inequality violations.

Measurement dependence varies with different hidden variable models.

Abstract

Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement independence. Weakening this assumption could alter the inequalities to accommodate experimental data whilst maintaining local interactions. A natural avenue for achieving this would be to model measurement as a dynamical process involving an interaction between the system and its environment (the measurement apparatus), that drives the hidden variables towards attractors representing measurement outcomes of the observable. Implementing such hidden variable dynamics, we can infer from observed correlations the hidden variable probability distributions before measurement, which differ according to which measurement settings were chosen. We explore various models of the dynamics of the hidden variables under measurement, revealing features that can create measurement dependence and others that can not.