Parameter Dependence and Bell nonlocality

TL;DR

This paper investigates the limits of classical models in reproducing quantum correlations under certain assumptions, identifying optimal bounds related to parameter dependence using symbolic optimization.

Contribution

It derives the optimal bounds for models saturating CHSH inequality with outcome and measurement independence, allowing parameter dependence, and verifies a previously proposed model as optimal.

Findings

Bound as a function of parameter dependence is established.

The model by [New Journal of Physics,12(8):083051] is shown to be optimal.

Symbolic optimization tools effectively find saturating models.

Abstract

Bell's theorem asserts that no model that satisfies all of the plausible physical assumptions of outcome independence (OI), measurement independence (MI) and Parameter Independence (PI) can reproduce quantum mechanics. Here I find the optimum model that saturates CHSH inequality for the case that outcome independence and measurement independence hold but parameter dependence is allowed. I find the bound as a function of a measure of parameter dependence and show that the model proposed by [New Journal of Physics,12(8):083051] is optimal for one-way parameter dependence. The symbolic optimizations to find the saturating models are performed using the open source software Analytical Optimizer v1.0.