Coincidence postselection for genuine multipartite nonlocality: Causal diagrams and threshold efficiencies

TL;DR

This paper investigates how to close the detection loophole in demonstrations of genuine multipartite nonlocality using coincidence postselection, causal diagrams, and threshold efficiencies, ensuring valid nonlocality tests even with imperfect detectors.

Contribution

It introduces a method to close the detection loophole in GMN experiments by employing causal diagrams and threshold efficiencies, applicable to realistic noisy devices.

Findings

Coincidence postselection cannot create loopholes with ideal devices.

Sharpened Bell inequalities can be valid after postselection with sufficient efficiency.

Genuine N-partite nonlocality can be demonstrated with independent sources and non-ideal detectors.

Abstract

Genuine multipartite nonlocality (GMN), the strongest form of multipartite nonlocality that describes fully collective nonlocal correlations among all experimental parties, can be observed when different distant parties each locally measure a particle from a shared entangled many-particle state. For the demonstration of GMN, the experimentally observed statistics are typically postselected: Events for which some parties do not detect a particle must be discarded. This coincidence postselection generally leads to the detection loophole that invalidates a proper nonlocality demonstration. In this work, we address how to close the detection loophole for a coincidence detection in demonstrations of nonlocality and GMN. We first show that if the number of detected particles is conserved, i.e., using ideal and noiseless experimental devices, one can employ causal diagrams and the no-signalling principle to prove that a coincidence postselection cannot create any detection loophole. Furthermore, for realistic experimental devices with finite detection efficiencies, we show how a general Bell inequality can be sharpened such that its new version is still valid after a postselection of the measurement data. In this case, there are threshold detection efficiencies that, if surpassed in the experiment, lead to the possibility to demonstrate nonlocality and GMN without opening the detection loophole. Our results imply that genuine $N$-partite nonlocality can be generated from $N$ independent particle sources even when allowing for non-ideal detectors.