The influence of the choice of post-processing method on Bell inequalities

TL;DR

This paper investigates how different post-processing methods in Bell inequality experiments affect critical detection efficiency, inequality equivalence, and non-signaling, highlighting the importance of choosing optimal strategies for various detector efficiencies.

Contribution

It analyzes the impact of post-processing choices on Bell inequality tests and identifies optimal strategies depending on detector efficiency ranges.

Findings

Post-processing affects critical detection efficiency thresholds.

Different strategies are optimal for different detector efficiencies.

Choice of post-processing influences the applicability of non-signaling principles.

Abstract

In every experimental test of a Bell inequality, we are faced with the problem of inefficient detectors. How we treat the events when no particle was detected has a big influence on the properties of the inequality. In this work, we study this influence. We show that the choice of post-processing can change the critical detection efficiency, the equivalence between different inequalities or the applicability of the non-signaling principle. We also consider the problem of choosing the optimal post-processing strategy. We show that this is a non-trivial problem and that different strategies are optimal for different ranges of detector efficiencies.