Inequalities for complementarity in observed statistics

TL;DR

This paper develops inequalities to analyze complementarity in observed statistics, linking violations to the absence of a joint distribution for incompatible observables, demonstrated through a Young interferometer example.

Contribution

It introduces a classical model with inequalities to test complementarity, connecting violations to the non-existence of joint distributions for incompatible observables.

Findings

Violations of inequalities indicate lack of joint distribution.

Inequalities can be tested with unsharp measurements.

Illustrated using path-interference duality in Young interferometer.

Abstract

We provide an analysis of complementarity via a suitably designed classicalmodel that leads to a set of inequalities that can be tested by means ofunsharp measurements. We show that, if the measured statistics does notfulfill the inequalities it is equivalent to the lack of a joint distribution for theincompatible observables. This is illustrated by path-interference duality ina Young interferometer.