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Structure of the algebra generated by a noncommutative operator graph which demonstrates the superactivation phenomenon for zero-error capacity. (English. Russian original) Zbl 1348.81129

Math. Notes 99, No. 6, 924-927 (2016); translation from Mat. Zametki 99, No. 6, 929-932 (2016).
From the introduction: M. E. Shirokov [Quantum Inf. Process. 14, No. 8, 3057–3074 (2015; Zbl 1327.81098)] recently suggested a construction of a noncommutative operator graph, depending on a complex parameter \(\theta\), which enables one to construct channels with positive quantum capacity for which the \(n\)-shot capacity is zero. We study the algebraic structure of this graph. Relations for the algebra generated by the graph are derived. In the limit case \(\theta = \pm 1\), the graph becomes commutative and degenerates into the direct sum of four one-dimensional irreducible representations of the Klein group.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A40 Channel models (including quantum) in information and communication theory
46L07 Operator spaces and completely bounded maps
46L10 General theory of von Neumann algebras
46L30 States of selfadjoint operator algebras
46L60 Applications of selfadjoint operator algebras to physics
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)

Citations:

Zbl 1327.81098
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Full Text: DOI

References:

[1] Shirokov, M. E., No article title, Quantum Inf. Process., 14, 3057 (2015) · Zbl 1327.81098 · doi:10.1007/s11128-015-1014-0
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