Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 304–308 | Cite as

On General Properties of Non-Commutative Operator Graphs



In this paper we study the general properties of non-commutative operator graphs. The problem of the existence of quantum anticliques is considered. The covariant property for the resolution of the identity which generates the graph is investigated.


Non-commutative operator graphs quantum anticliques 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. D. Choi and E. G. Effros, “Injectivity and operator spaces,” J. Funct. Anal. 24, 156–209 (1977).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    R. Duan, S. Severini, and A. Winter, “Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovasz theta function,” IEEE Trans. Inf. Theory 59, 1164–1174 (2013).CrossRefMATHGoogle Scholar
  3. 3.
    N. Weaver, “A’ quantum’ Ramsey theorem for operator systems,” Proc. Am. Math. Soc. 145, 4595–4605 (2017).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    E. Knill, R. Laflamme, and L. Viola, “Theory of quantum error correction for general noise,” Phys. Rev. Lett. 84, 2525–2528 (2000).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    R. Duan, “Super-activation of zero-error capacity of noisy quantum channels,” arXiv: 0906.2527 (2009).Google Scholar
  6. 6.
    M. E. Shirokov and T. V. Shulman, “On superactivation of zero-error capacities and reversibility of a quantum channel,” Commun. Math. Phys. 335, 1159–1179 (2015).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    G. G. Amosov and A. S. Mokeev, “On construction of anticliques for non-commutative operator graphs,” Zap. Nauchn. Sem.SPb.Otd. Mat. Inst. SteklovaPOMI 456, 5–15 (2017).Google Scholar
  8. 8.
    A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Edizione della Normale, Pisa, 2001).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

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

Personalised recommendations