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

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Abstract

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.

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Acknowledgements

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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  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    G. G. Amosov & A. S. Mokeev

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  1. G. G. Amosov
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  2. A. S. Mokeev
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Correspondence to G. G. Amosov.

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Amosov, G.G., Mokeev, A.S. On non-commutative operator graphs generated by covariant resolutions of identity. Quantum Inf Process 17, 325 (2018). https://doi.org/10.1007/s11128-018-2072-x

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