Particle states are equidistant to wave and fully-entangled states in an interferometer

TL;DR

This paper reveals that in a two-arm interferometer, pure particle states are geometrically equidistant from all states with the same path distinguishability, unlike wave or entangled states, highlighting a unique geometric property of particles.

Contribution

It introduces a geometric characterization of quantum states in interferometers, showing particles are equidistant from all states with the same distinguishability, unlike waves or entangled states.

Findings

Particle states are equidistant from all states with the same distinguishability.

Bures distance depends only on distinguishability for particles.

Wave and entanglon distances depend on additional parameters.

Abstract

In this article we show that, in a two-arm interferometer, pure quantum states of perfect path distinguishability (particles) are geometrically equidistant from all states with constant path distinguishability D. This property is not shared by other states, such as perfect fringe-visibility (waves) or maximally entangled quantum states (entanglon). Indeed, the Bures distance between a particle and any other state depends only the distinguishability of the latter. On the contrary, the Bures distance between a wave or an entanglon, and any other single photon state depends on other set of parameters.