Mutually unbiased bases and semi-definite programming

Stefan Weigert, Steve Brierley

Research output: Contribution to journalArticle (Academic Journal)

22 Citations (Scopus)

Abstract

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
JournalJournal of Physics: Conference Series
Volume254
Issue number1
DOIs
Publication statusPublished - 17 Dec 2010

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