2010/06/01 by Stephen Brierley, Stefan Weigert · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms #Polynomial and algebraic computation #math-ph #math.MP #math.OC #quant-ph
paper · pdf · doi:10.1088/1742-6596/254/1/012008
published as J. Phys.: Conf. Ser. 254 012008 (2010) · 11 pages,
arxiv created 2010/06/01 · openalex publication_date 2010/11/01 · arxiv updated 2011/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.