Coherence, Path-Predictability and I-Concurrence: A Triality

TL;DR

This paper introduces a new interference visibility based on Hilbert-Schmidt coherence, demonstrating its effectiveness in quantifying wave nature and its relation to predictability and entanglement in multipath quantum interference.

Contribution

It proposes a novel coherence-based visibility and a generalized predictability, establishing a triality relation that highlights entanglement's role in multipath quantum complementarity.

Findings

New coherence-based visibility effectively quantifies wave nature.

Generalized predictability reduces to known predictability for two paths.

Visibility, predictability, and entanglement follow a tight triality relation.

Abstract

It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. A new interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature, and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin, for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability and the I-concurrence (quantifying the entanglement between the quanton and the path-detector), are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity, for the first time.