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arXiv · 1006.0093

Mutually Unbiased Bases and Semi-definite Programming

Stephen Brierley·Stefan Weigert
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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 Grobner 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.

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Stephen Brierley, Stefan Weigert. 2010-06-01. Mutually Unbiased Bases and Semi-definite Programming. https://doi.org/10.1088/1742-6596%2F254%2F1%2F012008

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