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

Tomasz Paterek, Borivoje Dakić, and Časlav Brukner
Phys. Rev. A 79, 012109 – Published 16 January 2009

Abstract

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.

  • Received 14 April 2008

DOI:https://doi.org/10.1103/PhysRevA.79.012109

©2009 American Physical Society

Authors & Affiliations

Tomasz Paterek1, Borivoje Dakić1,2, and Časlav Brukner1,2

  • 1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
  • 2Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

Comments & Replies

Comment on “Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models”

Joanne L. Hall and Asha Rao
Phys. Rev. A 83, 036101 (2011)

Reply to “Comment on ‘Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models’ ”

Tomasz Paterek, Borivoje Dakić, and Časlav Brukner
Phys. Rev. A 83, 036102 (2011)

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Vol. 79, Iss. 1 — January 2009

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