ON THE IMPOSSIBILITY TO EXTEND TRIPLES OF MUTUALLY UNBIASED PRODUCT BASES IN DIMENSION SIX
Daniel McNulty, Stefan Weigert · International Journal of Quantum Information · 2012
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.