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Cryptography and Communications

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01-09-2010

Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power

MOLS and MUBs in odd prime power dimensions

Authors: Asha Rao, Diane Donovan, Joanne L. Hall

Published in: Cryptography and Communications | Issue 2/2010

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Abstract

There has been much interest in mutually unbiased bases (MUBs) and their connections with various other discrete structures, such as projective planes, mutually orthogonal Latin squares (MOLS) etc. It has been conjectured by Saniga et al. (J Opt B Quantum Semiclass Opt 6:L19–L20, 2004) that the existence of a complete set of MUBs in ℂ^d is linked to the existence of a complete set of MOLS of side length d. Since more is known about MOLS than about MUBs, most research has concentrated on constructing MUBs from MOLS (Roy and Scott, J Math Phys 48:072110, 2007; Paterek et al., Phys Rev A 70:012109, 2009). This paper gives a simple algebraic construction of MOLS from two known constructions of MUBs in the odd prime power case.

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Title: Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power
MOLS and MUBs in odd prime power dimensions
Authors: Asha Rao
Diane Donovan
Joanne L. Hall
Publication date: 01-09-2010
Publisher: Springer US
Published in: Cryptography and Communications / Issue 2/2010
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-010-0027-x

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