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

MOLS and MUBs in odd prime power dimensions

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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 ℂd 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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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments, which have made this paper more readable.

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Authors and Affiliations

  1. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia

    Asha Rao & Joanne L. Hall

  2. Department of Mathematics, University of Queensland, Brisbane, Australia

    Diane Donovan

Authors
  1. Asha Rao
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  2. Diane Donovan
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  3. Joanne L. Hall
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Correspondence to Asha Rao.

Additional information

Dedicated to Warwick de Launey, on the occasion of his 50th birthday.

Part of this work was carried out while D. Donovan was visiting RMIT University in August 2009.

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Rao, A., Donovan, D. & Hall, J.L. Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power. Cryptogr. Commun. 2, 221–231 (2010). https://doi.org/10.1007/s12095-010-0027-x

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  • DOI: https://doi.org/10.1007/s12095-010-0027-x

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