TY - JOUR

T1 - On inner geometry of noncommutative operator graphs

AU - Amosov, G. G.

N1 - Funding Information: This work was funded by the Ministry of Science and Higher Education of the Russian Federation (grant number 075-15-2020-788). Publisher Copyright: © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Operator systems (noncommutative operator graphs in other terminology) play a major role in the theory of quantum error correcting codes. Any operator graph is associated with a number of quantum channels. The possibility to transmit quantum information through a quantum channel with zero error is determined by the geometrical properties of the corresponding graph. Noncommutative operator graphs are known to be generated by positive operator-valued measures (POVMs). In turn, many principal POVMs consist of multiple of projections. We construct the model in which the graph is a linear envelope of two projection-valued resolutions of identities in a Hilbert space. Conditions for the existence of quantum anticliques (error-correcting codes) for the graph are investigated. The connection with Shirokov’s example of quantum superactivation (Shirokov in Probl Inform Transm 51(2):87–102, 2015; Shirokov and Shulman in Commun Math Phys 335:1159, 2015) is revealed.

AB - Operator systems (noncommutative operator graphs in other terminology) play a major role in the theory of quantum error correcting codes. Any operator graph is associated with a number of quantum channels. The possibility to transmit quantum information through a quantum channel with zero error is determined by the geometrical properties of the corresponding graph. Noncommutative operator graphs are known to be generated by positive operator-valued measures (POVMs). In turn, many principal POVMs consist of multiple of projections. We construct the model in which the graph is a linear envelope of two projection-valued resolutions of identities in a Hilbert space. Conditions for the existence of quantum anticliques (error-correcting codes) for the graph are investigated. The connection with Shirokov’s example of quantum superactivation (Shirokov in Probl Inform Transm 51(2):87–102, 2015; Shirokov and Shulman in Commun Math Phys 335:1159, 2015) is revealed.

UR - http://www.scopus.com/inward/record.url?scp=85094650625&partnerID=8YFLogxK

U2 - 10.1140/epjp/s13360-020-00871-1

DO - 10.1140/epjp/s13360-020-00871-1

M3 - Article

AN - SCOPUS:85094650625

VL - 135

JO - European Physical Journal Plus

JF - European Physical Journal Plus

SN - 2190-5444

IS - 10

M1 - 865

ER -