On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg-Weyl group
arXiv:1812.02515 · doi:10.1007/s10773-018-3963-4
Abstract
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.
9 pages