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arXiv · 0910.1439

On the connection between mutually unbiased bases and orthogonal Latin squares

T. Paterek·M. Pawlowski·M. Grassl·C. Brukner
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Abstract

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.

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T. Paterek, M. Pawlowski, M. Grassl, C. Brukner. 2009-10-08. On the connection between mutually unbiased bases and orthogonal Latin squares. https://doi.org/10.1088/0031-8949%2F2010%2Ft140%2F014031

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