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arXiv · 2604.06072

A multigraph approach to confusability in quantum channels

Sk Asfaq Hossain·Angshuman Bhattacharya
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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.

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Sk Asfaq Hossain, Angshuman Bhattacharya. 2026-04-07. A multigraph approach to confusability in quantum channels. https://arxiv.org/abs/2604.06072

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