Information complementarity: A new paradigm for decoding quantum incompatibility

TL;DR

This paper introduces an information-theoretic and geometric framework for understanding quantum incompatibility, providing universal criteria for detecting incompatible observables and new insights into fundamental quantum phenomena.

Contribution

It develops a novel paradigm combining information theory and geometry to decode quantum incompatibility, offering universal detection criteria and measures applicable to various observables.

Findings

Universal criteria for detecting incompatible observables

A natural measure of quantum incompatibility

New measurement uncertainty relations and insights into wave-particle duality

Abstract

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality. However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many researchers. Here we introduce an information theoretic paradigm together with an intuitive geometric picture for decoding incompatible observables, starting from two simple ideas: Every observable can only provide limited information and information is monotonic under data processing. By virtue of quantum estimation theory, we introduce a family of universal criteria for detecting incompatible observables and a natural measure of incompatibility, which are applicable to arbitrary number of arbitrary observables. Based on this framework, we derive a family of universal measurement uncertainty relations, provide a simple information theoretic explanation of quantitative wave--particle duality, and offer new perspectives for understanding Bell nonlocality, contextuality, and quantum precision limit.