Detection Loophole in Bell experiments: How post-selected local correlations can look non-local

TL;DR

This paper investigates how post-selection in Bell experiments can create apparent non-local correlations from local models, highlighting the detection loophole's impact on interpreting quantum non-locality.

Contribution

It characterizes the set of post-selected local correlations as a polytope larger than the Bell local polytope, providing new insights into the detection loophole.

Findings

Post-selected local correlations form a larger polytope than the Bell local polytope.

Facets of the post-selected local polytope are characterized in the CHSH scenario.

Analysis offers new understanding of the detection loophole in Bell tests.

Abstract

A common problem in Bell type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply post-selects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all post-selected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this post-selected local polytope in the CHSH scenario, where two parties have binary inputs and outcomes. Our approach gives new insights on the detection loophole problem.