# ON THE IMPOSSIBILITY TO EXTEND TRIPLES OF MUTUALLY UNBIASED PRODUCT BASES IN DIMENSION SIX

@article{McNulty2012ONTI, title={ON THE IMPOSSIBILITY TO EXTEND TRIPLES OF MUTUALLY UNBIASED PRODUCT BASES IN DIMENSION SIX}, author={D. McNulty and S. Weigert}, journal={International Journal of Quantum Information}, year={2012}, volume={10}, pages={1250056} }

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… Expand

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