Mutually unbiased bases and semi-definite programming

Stefan Weigert, Steve Brierley

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)


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
Issue number1
Publication statusPublished - 17 Dec 2010


Dive into the research topics of 'Mutually unbiased bases and semi-definite programming'. Together they form a unique fingerprint.

Cite this