Duality of Quantum Coherence and Path Distinguishability

TL;DR

This paper establishes a generalized duality relation for multipath quantum interference, linking quantum coherence and path distinguishability, extending the wave-particle duality concept beyond two-path systems and accounting for decoherence effects.

Contribution

It introduces a unified framework connecting quantum coherence and path distinguishability for arbitrary multipath interference, generalizing existing duality relations.

Findings

Duality relation holds for arbitrary multipath interference.

Quantum coherence quantified as normalized coherence relates to fringe visibility.

Relation remains valid under decoherence effects.

Abstract

We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.