Quantum coherence and negative quasi probabilities in a contextual three-path interferometer

TL;DR

This paper explores quantum coherence and non-classical correlations in a three-path interferometer, demonstrating how negative quasi-probabilities relate to measurement contexts and state classification.

Contribution

It introduces a new method to classify pure states in a three-dimensional Hilbert space using orthogonality relations and negative Kirkwood-Dirac distributions.

Findings

Negative quasi-probabilities indicate non-classical correlations.

Orthogonality relations classify states based on measurement contexts.

The approach links quantum coherence to measurement-induced non-classicality.

Abstract

Basic quantum effects are often illustrated using single particle interferences in two-path interferometers. A wider range of non-classical phenomena can be illustrated using three-path interferometers, but the increased complexity of quantum statistics in a three-dimensional Hilbert space makes it difficult to identify a representative set of observable properties that could be used to characterize specific phenomena. Here, I propose a characterization of pure states based on a five-stage interferometer recently introduced to demonstrate the relation between different measurement contexts (Optica Quantum 1, 63 (2023)). It is shown that the orthogonality relations between the states representing the different measurement contexts can be used to classify pure states within the three-dimensional Hilbert space according to the non-classical correlations between different contexts expressed by negative Kirkwood-Dirac distributions.