Operator system characterizations of SIC-POVMs and mutually unbiased bases
Abstract
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension d if and only if there exists a d2-dimensional operator system satisfying certain order-theoretic conditions. We also describe a method of constructing such an operator system and demonstrate that the first step of this construction can be carried out successfully. We obtain analogous results for the existence of d+1 mutually unbiased bases in a given dimension.
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