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Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation

Discrete phase-space approach to mutually orthogonal Latin squares

arXiv
Authors: Mario Gaeta, Olivia Di Matteo, Andrei B. Klimov, Hubert de Guise

Year

2014

Paper ID

47860

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

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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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1408.6742 [2] arXiv https://arxiv.org/abs/1408.6742 [3] Publisher https://arxiv.org/abs/1408.6742

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