Bell and EPR experiments with signalling data

TL;DR

This paper introduces extended models allowing bounded signalling to account for experimental imperfections in Bell and EPR experiments, providing new tests for non-classicality applicable to real quantum data.

Contribution

It develops methods to incorporate bounded signalling into local hidden variable and local hidden state models, extending traditional non-signalling assumptions.

Findings

Applicable to IBM quantum processor data

Effective in post-selected inefficient detector data

Provides corrected Bell and steering inequalities

Abstract

The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here, we propose extensions of local hidden variable and local hidden state theories that allow for bounded, operationally quantifiable, amounts of signalling. We show how non-classicality tests can be developed for these models, both through exact methods based on the full set of observed statistics and through corrections to the standard Bell and steering inequalities. We demonstrate the applicability of these methods via two scenarios that feature apparent signalling: an IBM quantum processor and post-selected data from inefficient detectors.