Article ID Journal Published Year Pages File Type
5500410 Reports on Mathematical Physics 2017 19 Pages PDF
Abstract

The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the question whether two Lagrangian Clifford tori intersect, and a body of results exists concerning it. These results are however rather weak from the point of view of the first problem. We make a detailed study of how the intersections behave in the simplest nontrivial case, that of complex projective 2-space (the qutrit), for which the set of pairs of Clifford tori can be usefully parametrized by the unistochastic subset of Birkhoff's polytope. Pairs that do not intersect transversally are located. Some calculations in higher dimensions are included to see which results are special to the qutrit.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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