Bell Inequalities for Continuously Emitting Sources

TL;DR

This paper introduces a new family of Bell inequalities based on distance measures between recorded timetags, addressing the coincidence loophole caused by timing jitter in experiments with continuously emitted entangled photon pairs.

Contribution

The authors develop distance-based Bell inequalities that are robust against timing jitter and settings-dependent errors, improving the reliability of non-classical correlation tests.

Findings

Bell inequalities based on signed, directed distances can unambiguously demonstrate non-classical correlations.

The method improves the signal-to-noise ratio in Bell tests with continuous photon streams.

Systematic modifications of Bell functions enhance the significance of violations.

Abstract

A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have "jitter", coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-realistic system to show apparent violation--the so-called "coincidence loophole". Here we introduce a family of Bell inequalities based on signed, directed distances between the parties' sequences of recorded timetags. Given that the timetags are recorded for synchronized, fixed observation periods and that the settings choices are random and independent of the source, violation of these inequalities unambiguously shows non-classical correlations violating local realism. Distance-based Bell inequalities are generally useful for two-party configurations where the effective size of the measurement outcome space is large or infinite. We show how to systematically modify the underlying Bell functions to improve the signal to noise ratio and to quantify the significance of the violation.