Statistical analysis of Bell tests via generalized measurements

TL;DR

This paper presents a comprehensive statistical framework for analyzing Bell test results that accounts for noise introduced by simultaneous measurements of all observables, enhancing the robustness of quantum nonlocality tests.

Contribution

It introduces a method to incorporate measurement noise into Bell test analysis, either by adapting Bell bounds or through data inversion, applicable in practical experimental setups.

Findings

Both strategies yield consistent results in noise handling.

The approach improves the reliability of Bell test conclusions under realistic conditions.

The methods are applicable to experiments with simultaneous measurements of observables.

Abstract

We provide a fully statistical analysis of the results of a Bell test beyond mean values. This is possible in a practical scheme where all the observables involved in the test are simultaneously measured at the expense of unavoidably additional noise. To deal with this noise we can follow two strategies leading to the same results. These are to adapt the Bell bound to include the noise, or to remove the additional noise via suitable data inversion.