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.

翻译：我们提出了一种研究量子信道混淆性的新方法，即量子混淆多重图，该方法将输出信息融入图结构。通过"计数"该混淆多重图中两个顶点之间的边数，即可恢复传统的信道混淆性"单边"图。基于这一物理动机，我们从Weaver量子关系的视角发展了量子多重图理论，并探究了其量子图论性质。最后，我们给出了刻画那些可作为量子混淆多重图的量子多重图的充要条件。