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arXiv · 1812.02515

On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg-Weyl group

G. G. Amosov·A. S. Mokeev
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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.

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G. G. Amosov, A. S. Mokeev. 2018-12-06. On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg-Weyl group. https://doi.org/10.1007/s10773-018-3963-4

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