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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 2 — Feb. 1, 2007
  • pp: 371–378

Mutually unbiased bases and discrete Wigner functions

Gunnar Björk, José L. Romero, Andrei B. Klimov, and Luis L. Sánchez-Soto  »View Author Affiliations


JOSA B, Vol. 24, Issue 2, pp. 371-378 (2007)
http://dx.doi.org/10.1364/JOSAB.24.000371


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Abstract

Mutually unbiased bases and discrete Wigner functions are closely but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime N = d n , which describes a composite system of n qudits. Hence, entanglement naturally enters the picture. Although our results are general, we concentrate on the simplest nontrivial example of dimension N = 8 = 2 3 . It is shown that the number of fundamentally different Wigner functions is severely limited if one simultaneously imposes translational covariance and that the generating operators consist of rotations around two orthogonal axes, acting on the individual qubits only.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(270.0270) Quantum optics : Quantum optics

ToC Category:
Quantum Information

History
Original Manuscript: May 19, 2006
Revised Manuscript: August 3, 2006
Manuscript Accepted: August 18, 2006
Published: January 26, 2007

Citation
Gunnar Björk, José L. Romero, Andrei B. Klimov, and Luis L. Sánchez-Soto, "Mutually unbiased bases and discrete Wigner functions," J. Opt. Soc. Am. B 24, 371-378 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-2-371

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