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

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.

Figures (2)

• Figure 1: Contextual three-path interferometer. The reflectivities must be adjusted so that the output paths correspond to the input paths as shown. Here, I will consider the case of $R_1=R_2=1/2$, $R_{S1}=R_{S2}=1/3$, and $R_f=1/4$.
• Figure 2: Illustration of Hilbert space directions corresponding to the ten paths in the contextual interferometer. Each great circle shown indicates orthogonality to one of the ten path states. Outer path states are found at the intersection of four great circles and inner path states are found at the intersection of two great circles. In addition, ten more states can be defined by orthogonality relations that are not satisfied by specific path states.