Orthogonality for quantum Latin isometry squares

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Goyeneche et al recently proposed a notion of orthogonality for quantum Latin squares, and showed that orthogonal quantum Latin squares yield quantum codes. We give a simplified characterization of orthogonality for quantum Latin squares, which we show is equivalent to the existing notion. We use this simplified characterization to give an upper bound for the number of mutually orthogonal quantum Latin squares of a given size, and to give the first examples of orthogonal quantum Latin squares that do not arise from ordinary Latin squares. We then discuss quantum Latin isometry squares, generalizations of quantum Latin squares recently introduced by Benoist and Nechita, and define a new orthogonality property for these objects, showing that it also allows the construction of quantum codes. We give a new characterization of unitary error bases using these structures


Original languageEnglish
Pages (from-to)253–266
JournalElectronic Proceedings in Theoretical Computer Science, EPTCS
Publication statusPublished - 31 Jan 2019
Event15th International Conference on Quantum Physics and Logic (QPL 2018) - Dalhousie University, Halifax, Canada
Duration: 3 Jun 20187 Jun 2018