Relaxed Bell inequalities as a trade-off relation between measurement dependence and hiddenness

TL;DR

This paper introduces a new trade-off relation between hiddenness and measurement dependence in local hidden variable theories, extending Bell inequalities to quantify assumption violations.

Contribution

It provides a novel quantification of hidden variables and derives a new trade-off relation applicable to any local hidden variable theory.

Findings

Derived a new trade-off relation between hiddenness and measurement dependence.

Extended Bell inequalities to include quantification of assumption violations.

Applicable to all local hidden variable theories.

Abstract

Quantum correlations that violate the Bell inequality cannot be explained by any (measurement independent) local hidden variable theory. However, the violation only implies incompatibility of the underlying assumptions of reality, locality, and measurement independence, and does not address the extent to which each assumption is violated quantitatively. In contrast, Hall (2010,2011) gave a quantification of each assumption and generalized the Bell-CHSH inequality that gives a trade-off relationship between the underlying assumptions. In this paper, we introduce a quantification of hidden variables (hiddenness) and derive a new trade-off relation between the hiddenness and the measurement dependency that holds for any local hidden variable theory.