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arXiv:1111.3849 · Journal of Physics A Mathematical and Theoretical

The limited role of mutually unbiased product bases in dimension 6

Daniel McNulty, Stefan Weigert

Published Feb 21, 2012• 37 citations
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Abstract

We show that a complete set of seven mutually unbiased bases in dimension six, if it exists, cannot contain more than one product basis.
DOI
10.1088/1751-8113/45/10/102001

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Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power, i.e. in composite dimensions such as six or ten. Fourteen mathematically equivalent formulations of the existence problem are presented. We comprehensively summarise analytic, computer-aided and numerical results relevant to the case of composite dimensions. Known modifications of the existence problem are reviewed and potential solution strategies are outlined.