A generalized wave-particle duality relation for finite groups

TL;DR

This paper introduces a generalized wave-particle duality relation using group asymmetry, linking quantum coherence, group actions, and irreducible representations to deepen understanding of quantum complementarity.

Contribution

It derives a new duality relation involving group asymmetry, connecting quantum coherence measures with group representation theory.

Findings

Duality relation involving group asymmetry and irreducible representations

Relation to success probability in group element discrimination

Enhanced understanding of wave-particle duality in quantum systems

Abstract

Wave-particle duality relations express the fact that knowledge about the path a particle took suppresses information about its wave-like properties, in particular, its ability to generate an interference pattern. Recently, duality relations in which the wave-like properties are quantified by using measures of quantum coherence have been proposed. Quantum coherence can be generalized to a property called group asymmetry. Here we derive a generalized duality relation involving group asymmetry, which is closely related to the success probability of discriminating between the actions of the elements of a group. The second quantity in the duality relation, the one generalizing which-path information, is related to information about the irreducible representations that make up the group representation.