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arXiv · 1408.6742

Discrete phase-space approach to mutually orthogonal Latin squares

Mario Gaeta·Olivia Di Matteo·Andrei B. Klimov·Hubert de Guise
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Abstract

We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial sets into isomorphisms of Latin squares, and find a general form of permutations that map between Latin squares corresponding to unitarily equivalent mutually unbiased sets. We extend this result to a conjecture: MOLS associated to unitarily equivalent MUBs will always be isomorphic, and MOLS associated to unitarily inequivalent MUBs will be non-isomorphic.

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Mario Gaeta, Olivia Di Matteo, Andrei B. Klimov, Hubert de Guise. 2014-08-28. Discrete phase-space approach to mutually orthogonal Latin squares. https://doi.org/10.1088/1751-8113/47/43/435303

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