On non-commutative operator graphs generated by covariant resolutions of identity
arXiv:1809.08586
Abstract
We study non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary representations of a compact group. Our main goal is searching for orthogonal projections which are anticliques (error-correcting codes) for such graphs. A special attention is paid to the covariance with respect to unitary representations of the circle group. We determine a tensor product structure in the space of representation under which the obtained anticliques are generated by entangled vectors.
13 pages, based upon the talk at International conference "Quantum information, statistics, probability" with a special session dedicated to A. S. Holevo's 75-th birthday