A multigraph approach to confusability in quantum channels

TL;DR

This paper introduces quantum confusability multigraphs, a new graphical framework for analyzing confusability in quantum channels, extending traditional models by incorporating output information.

Contribution

It develops a theory of quantum multigraphs based on Weaver's quantum relations and characterizes which multigraphs correspond to quantum confusability structures.

Findings

Established a new quantum multigraph framework for channel confusability

Connected multigraph edge counting to traditional confusability graphs

Provided a characterization criterion for quantum confusability multigraphs

Abstract

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.