Efficient quantification of experimental evidence against local realism

TL;DR

This paper presents an efficient protocol for computing bounds on the probability of observing violations of local realism, enhancing the robustness and confidence in quantum tests involving Bell inequalities across various scenarios.

Contribution

It introduces a general, efficient method for deriving bounds from Bell inequalities applicable to multiple parties, settings, and outcomes, improving upon previous approaches.

Findings

Protocol computes bounds efficiently for any Bell inequality setup.

Applicable to tests of entanglement and dimensionality.

Enhances confidence in experimental violations of local realism.

Abstract

Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local realism and determine a bound on the probability, according to local realism, of obtaining a violation at least that observed. In general, it is difficult to obtain sufficiently robust and small bounds. Here we describe an efficient protocol for computing such bounds from any set of Bell inequalities for any number of parties, measurement settings, or outcomes. The protocol can be applied to tests of other properties (such as entanglement or dimensionality) that are witnessed by linear inequalities.