Generalized measurements for Bell tests in different probability spaces

TL;DR

This paper explores how Bell tests' statistical interpretations depend on the probability space used and introduces a versatile experimental scheme enabling new Bell tests through generalized measurements.

Contribution

It demonstrates a unified experimental approach applicable to different probability spaces and proposes novel Bell tests not feasible with standard methods.

Findings

A single experimental setup can be valid across multiple probability spaces.

Generalized measurements enable new Bell tests beyond traditional approaches.

The approach enhances the flexibility and interpretative power of Bell tests.

Abstract

Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and interpretations depend on the probability space adopted. Some other recent works have also shown that generalized measurements may allow to further exploit the statistics of Bell-like tests. Following these ideas, in this work we show that one and the same experimental arrangement can provide a practical scheme valid for two very different probability spaces. Moreover, we show that this allows the introduction of novel Bell tests that are not possible in more standard approaches.