Binarisation of multi-outcome measurements in high-dimensional quantum correlation experiments

TL;DR

This paper examines how converting multi-outcome quantum measurements into binary ones can create loopholes, potentially reducing observed quantum advantages, and emphasizes the need for accurate analysis and genuine multi-outcome measurements.

Contribution

It highlights the risks of binarising multi-outcome measurements in high-dimensional quantum experiments and provides methods to accurately analyze binarised data to preserve quantum features.

Findings

Binarisation can open loopholes in quantum correlation tests.

Binarisation may significantly reduce quantum advantages.

Accurate data analysis is crucial for revealing quantum features.

Abstract

High-dimensional systems are an important frontier for photonic quantum correlation experiments. These correlation tests commonly prescribe measurements with many possible outcomes but they are often implemented through many individual binary-outcome measurements that use only a single-detector. Here, we discuss how this binarisation procedure for multi-outcome measurements can open a loophole, unless specific device-characterisation assumptions are satisfied. We highlight that correlation tests designed for multi-outcome measurements can be trivialised in binarised implementations and we then show how to accurately analyse binarised data to reveal its quantum features. For seminal types of correlation experiments, such as Bell inequality tests, steering tests and prepare-and-measure experiments, we find that binarisation may incur a sizable cost in the magnitude of quantum advantages. This emphasizes the importance of both accurate data analysis and implementing genuinely multi-outcome measurements in high-dimensional correlation experiments.