Coherence and entropy complementarity relations of generalized wave-particle duality

TL;DR

This paper develops generalized measures for wave and particle properties in high-dimensional quantum systems, revealing deep connections between wave-particle duality, coherence, and quantum entropy through complementary relations.

Contribution

It introduces a unified framework using Morozova-Chentsov functions to quantify wave-particle duality and establish new complementary relations involving coherence and entropy.

Findings

Wave-particle duality quantified by generalized predictability and visibility measures.

Complementary relations connect visibility, predictability, and quantum f entropy.

Framework applicable to diverse functions for different duality scenarios.

Abstract

The concept of wave-particle duality holds significant importance in the field of quantum mechanics, as it elucidates the dual nature encompassing both wave-like and particle-like properties exhibited by microscopic particles. In this paper, we construct generalized measures for the predictability and visibility of $n$-path interference fringes to quantify the wave and particle properties in quantum high-dimensional systems. By employing the Morozova-Chentsov function, we ascertain that the wave-particle relationship can be delineated by the average coherence. This function exhibits a close correlation with the metric-adjusted skew information, thereby we establish complementary relations between visibility, predictability, and quantum $f$ entropy, which reveals deep connections between wave-particle duality and other physical quantities. Through our methodology, diverse functions can be selected to yield corresponding complementary relationships.