A multigraph approach to confusability in quantum channels
This work addresses a theoretical problem in quantum information theory, offering an incremental advancement in graphical representations for quantum channels.
The paper tackles the problem of analyzing confusability in quantum channels by introducing a new multigraph approach that incorporates output information, and it provides a necessary and sufficient condition for characterizing quantum confusability multigraphs.
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.