One Sided indeterminism alone is not a useful resource to simulate any nonlocal correlation

TL;DR

This paper investigates whether relaxing constraints on only one side of a bipartite system can simulate nonlocal correlations, concluding that one-sided indeterminism alone is insufficient without signaling or measurement dependence.

Contribution

The study derives Bell inequalities under one-sided relaxation and proves that randomness alone cannot produce nonlocal correlations without signaling.

Findings

One-sided randomness cannot violate Bell-CHSH inequalities.

Signaling and measurement dependence can simulate any nonlocal correlation.

The paper confirms a conjecture regarding one-sided relaxation scenarios.

Abstract

Determinism, no signaling and measurement independence are some of the constraints required for framing Bell inequality. Any model simulating nonlocal correlations must either individually or jointly give up these constraints. Recently M. J. W. Hall (Phys Review A, \textbf{84}, 022102 (2011)) derived different forms of Bell inequalities under the assumption of individual or joint relaxation of those constraints on both(i.e., two) the sides of a bipartite system. In this work we have investigated whether one sided relaxation can also be a useful resource for simulating nonlocal correlations or not. We have derived Bell-type inequalities under the assumption of joint relaxation of these constraints only by one party of a bipartite system. Interestingly we found that any amount of randomness in correlations of one party in absence of signaling between two parties is incapable of showing any sort of Bell-CHSH violation whereas signaling and measurement dependence individually can simulate any nonlocal correlations. We have also completed the proof of a recent conjecture due to Hall (Phys. Rev. A \textbf{82}, 062117 (2010); Phys. Rev. A \textbf{84}, 022102 (2011)) for one sided relaxation scenario only.