Nonclassical joint distributions and Bell measurements

TL;DR

This paper proposes a method for joint measurement of incompatible observables in Bell tests, allowing the extraction of individual statistics and identifying nonclassical behavior through the properties of the reconstructed joint distribution.

Contribution

It introduces a novel experimental approach for simultaneous measurement of incompatible observables and a data inversion technique to analyze nonclassical correlations.

Findings

Successful derivation of joint distributions from experimental data

Identification of nonclassical behavior via non-positive joint distributions

Potential to test Bell inequalities without traditional measurement incompatibility constraints

Abstract

Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of incompatible observables requires different experimen-tal procedures, which no necessarily must share a common joint statistics. In this work, we avoidthese difficulties by proposing a joint simultaneous measurement experiment. We can obtain theexact individual statistics of all the observables involved in the Bell inequalities after a suitable datainversion. A lack of positivity or any other pathology of the so retrieved joint distribution is then asignature of nonclassical behavior.