Operator system characterizations of SIC-POVMs and mutually unbiased bases
arXiv:2410.01119 · doi:10.1007/s00023-025-01633-4
Abstract
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension if and only if there exists a -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 mutually unbiased bases in a given dimension.
Final version. Published in Annales Henri Poincaré