Asymptotically optimal data analysis for rejecting local realism

TL;DR

This paper introduces a prediction-based-ratio (PBR) analysis protocol that provides valid, asymptotically optimal p-values for testing local realism in quantum experiments, even with varying states and memory effects.

Contribution

The authors develop a novel PBR method for analyzing violations of local realism that remains valid under arbitrary state variations and memory loopholes, improving statistical reliability.

Findings

PBR p-values are valid even with state variations and memory effects

Compared to standard methods, PBR provides asymptotically optimal p-values

PBR does not depend on specific Bell inequalities or experimental details

Abstract

Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p-value. We propose a prediction-based-ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p-values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, arXiv:quant-ph/0110137]. We find that the p-values of the former can be too small and are therefore not statistically valid, while those derived from the latter are sub-optimal. PBR p-values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.