Journal | J. Phys.: Conf. Ser. |
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Date | Published - 1 Dec 2010 |
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Issue number | 1 |
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Volume | 254 |
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Number of pages | 11 |
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Original language | English |
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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.