On the duality between homological quantum codes of a hypermap and its dual hypermap
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Publication:6366817
DOI10.1007/S11128-022-03797-YzbMath1509.81330arXiv2105.01608MaRDI QIDQ6366817
Publication date: 4 May 2021
Abstract: From a given topological hypermap $H$, we define two related hypermaps $H^ riangle$ and $H^
abla$ as complements of the ordinary dual hypermap $H^*$ along with the concepts of their edge hypermap quantum codes $mathcal{C}^ riangle$ and $mathcal{C}^ abla$. We then show that, when the sets of special darts are naturally corresponded, the duality between the ordinary hypermap quantum code $mathcal{C}$ from $H$ and the one $mathcal{C}^*$ from $H^*$ can be greatly simplified to the duality between $mathcal{C}^ riangle$ and $mathcal{C}^
abla$.
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