Mutually Unbiased Bases and Semi-definite Programming

Stephen Brierley, Stefan Weigert

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A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Gröbner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.
Original languageEnglish
Article number012008
Number of pages11
JournalJ. Phys.: Conf. Ser.
Issue number1
Publication statusPublished - 1 Dec 2010


  • Mathematical Physics

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