Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models

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Mutually unbiased bases encapsulate the concept of complementarity—the impossibility of simultaneous knowledge of certain observables—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 derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.
Original languageEnglish
Article number012109
Number of pages6
JournalPhysical Review A
Issue number1
Publication statusPublished - 2009

Austrian Fields of Science 2012

  • 103026 Quantum optics

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