Mutually Unbiased Bases and Orthogonal Latin Squares

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  • 14 April 2008
Abstract
Mutually unbiased bases encapsulate the concept of complementarity in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We use already existing knowledge about the squares to derive in a simple way all known results about the unbiased bases, find the lower bound on their number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Our results can be used to construct hidden-variable models which efficiently simulate results of complementary measurements on quantum systems with arbitrary dimension.

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