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On the structure of symmetric quantum measurements

Jon Yard, Microsoft Research Station Q

(Session 6c : Friday from 1:30 - 2:00)

Abstract. A central problem in quantum information theory is to understand the apparent existence, for any finite quantum system, of highly-symmetric optimal quantum measurements known as SIC-POVMs. These measurements correspond to finite sets of equiangular complex vectors of the maximal possible size. Much evidence points to the existence of SIC-POVMs obtained from orbits of finite Heisenberg groups, which are proved to exist for about 20 dimensions and which have been found numerically up to around dimension 60. In this talk, I will show how the mathematics of class field theory can explain the group-theoretic structure inherent to these known examples while offering predictions for their structure in arbitrary dimensions.