Generalized Bell Inequality Experiments and Computation

TL;DR

This paper explores the constraints of Bell inequalities in multi-party, multi-setting quantum experiments, revealing how local hidden variable theories relate to computational limitations and extending non-local box concepts.

Contribution

It introduces a computational framework to characterize Bell inequalities in complex settings and generalizes non-local boxes to many parties with multiple outcomes.

Findings

Local hidden variable theories have limited computational expressiveness.

Generalized non-local boxes for many parties and outcomes are proposed.

Pre-processing of measurement data can simulate non-local correlations outside binary settings.

Abstract

We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in a local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich non-local box for many parties and non-binary inputs and outputs at each site. Finally, we comment on the effect of pre-processing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally non-local correlations such as those of these generalised Popescu-Rohrlich non-local boxes.