Source-linked AI summary
Relations between coherence and path information
Emilio Bagan, Janos A. Bergou, Seth S. Cottrell, Mark Hillery
TL;DR
The paper studies how coherence and path information are related in multi-path interferometers. It derives an l1-coherence relation using detector-state discrimination and an entropic relation using relative-entropy coherence and mutual information.
Problem
Multi-path interferometers need coherence and path-information relations extending two-path visibility results and using detector-based path information.
Method
The paper uses normalized l1 coherence with minimum-error discrimination of detector states, and relative-entropy coherence with mutual information from measurements on detector states.
Results
The paper derives two multi-path duality relations connecting path information with l1 and entropic coherence measures.
Takeaways & Limitations
The l1 and entropic coherence measures are strong candidates for multi-path generalizations of the visibility-path-information relation.
Abstract
from arXiv · showhide
We find two relations between coherence and path-information in a multi-path interferometer. The first builds on earlier results for the two-path interferometer, which used minimum-error state discrimination between detector states to provide the path information. For visibility, which was used in the two-path case, we substitute a recently defined $l_{1}$ measure of quantum coherence. The second is an entropic relation in which the path information is characterized by the mutual information between the detector states and the outcome of the measurement performed on them, and the coherence measure is one based on relative entropy.