On non-commutative operator graphs generated by covariant resolutions of identity
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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.
KeywordsNon-commutative operator graphs Covariant resolutions of identity Quantum anticliques Entangled vectors
The authors are extremely grateful to the anonymous referee for a careful reading of the text and many fruitful remarks. This work is supported by the Russian Science Foundation under Grant 17-11-01388 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.
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