par Brierley, Stephen ;Weigert, Stefan
Référence Journal of physics. Conference series, 254, 1, 012008
Publication Publié, 2010
Référence Journal of physics. Conference series, 254, 1, 012008
Publication Publié, 2010
Article révisé par les pairs
Résumé : | 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. © 2010 IOP Publishing Ltd. |