A multigraph approach to confusability in quantum channels
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911573989130240 |
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| author | Hossain, Sk Asfaq Bhattacharya, Angshuman |
| author_facet | Hossain, Sk Asfaq Bhattacharya, Angshuman |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A multigraph approach to confusability in quantum channels Hossain, Sk Asfaq Bhattacharya, Angshuman Quantum Algebra Information Theory Functional Analysis Quantum Physics 46L07, 81P45, 46L08, 05C90 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. |
| title | A multigraph approach to confusability in quantum channels |
| topic | Quantum Algebra Information Theory Functional Analysis Quantum Physics 46L07, 81P45, 46L08, 05C90 |
| url | https://arxiv.org/abs/2604.06072 |