On non-commutative operator graphs generated by covariant resolutions of identity

In quantum information theory, operator systems are commonly called non-commutative operator graphs. Their elements are viewed as a source of errors that can occur in the transmission of information. The well-known problem of finding error-correcting codes (E. Knill, R. Laflamme' 1997) leads to the notion of a quantum anticlique. The report will describe the non-commutative operator graphs generated by reducible unitary representations of the circle group and the discrete Heisenberg-Weyl group, for which there are quantum anticliques.