A multigraph approach to confusability in quantum channels

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. Bycounting" 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.