# On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg-Weyl group. (arXiv:1812.02515v1 [quant-ph])

We consider a reducible unitary representation of Heisenberg-Weyl group in a
tensor product of two Hilbert spaces. A non-commutative operator graph
generated by this representation is introduced. It is shown that spectral
projections of unitaries in the representation are anticliques (quantum
error-correcting codes) for this graph. The obtained codes are appeared to be
linear envelopes of entangled vectors.