Discrete phase-space approach to mutually orthogonal Latin squares

Mario Gaeta, Olivia Di Matteo, Andrei B Klimov, Hubert de Guise
2014 Journal of Physics A: Mathematical and Theoretical  
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
more » ... ween 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.
doi:10.1088/1751-8113/47/43/435303 fatcat:pkta4g5aljgfbjxr446rfs5xsq