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arXiv · 1203.6887

On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

Daniel McNulty·Stefan Weigert
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Abstract

An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.

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Daniel McNulty, Stefan Weigert. 2012-10-01. On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six. https://doi.org/10.1142/s0219749912500566

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