Complementarity and the pathological statistics of the quantum impossible

TL;DR

This paper explores how imperfect measurements and data inversion can produce joint distributions for complementary quantum observables, revealing quantum features through the pathological aspects of these inferred distributions, exemplified by wave-particle duality.

Contribution

It introduces a method to derive joint distributions for complementary observables in quantum physics using imperfect measurements and data inversion, highlighting quantum-specific pathologies.

Findings

Inferred distributions exhibit non-classical pathologies.

Wave-particle duality analyzed through joint distribution pathologies.

Method demonstrates quantum complementarity effects in measurement data.

Abstract

Standard quantum physics prevents the existence of a joint statistics for complementary observables. Nevertheless, a joint distribution for complementary observables can be derived from their imperfect simultaneous measurement followed by a suitable data inversion. Quantumness is reflected then in the pathologies of the inferred distribution. We apply this program to the paradigmatic example of complementarity: the wave-particle duality in a Young interferometer.