Discrete phase-space approach to mutually orthogonal Latin squares
Quantum Physics
2014-12-24 v2
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.
Keywords
Cite
@article{arxiv.1408.6742,
title = {Discrete phase-space approach to mutually orthogonal Latin squares},
author = {Mario Gaeta and Olivia Di Matteo and Andrei B. Klimov and Hubert de Guise},
journal= {arXiv preprint arXiv:1408.6742},
year = {2014}
}