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

  • G. G. Amosov
  • A. S. Mokeev
Article
  • 39 Downloads

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.

Keywords

Non-commutative operator graphs Covariant resolutions of identity Quantum anticliques Entangled vectors 

Notes

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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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