Quasi-orthogonal decomposition of matrix algebras
Motivated by Quantum Information Theory, I investigate possible quasi-orthogonal decompositions of matrix algebras. Decomposing our matrix algebra, in particular, into maximal abelian subalgebras, is equivalent to finding a complete system of "mutually unbiased bases" (MUB) which is a famous open problem. However, the general case is little studied.
In my talk I will explain the origin of the problem, its surprising relation to such other problems as that of the existence of a complete set of orthogonal Latin squares, some known facts as well as some new results.