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Probl. Peredachi Inf., 2018, Volume 54, Issue 1, Pages 24–38 (Mi ppi2257)  

Information Theory

On the energy-constrained diamond norm and its application in quantum information theory

M. E. Shirokov

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

Abstract: We consider a family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates strong (pointwise) convergence on the set of all quantum channels (which is more adequate for describing variations of infinite-dimensional channels than the diamond norm topology). We obtain continuity bounds for information characteristics (in particular, classical capacities) of energy-constrained infinite-dimensional quantum channels (as functions of a channel) with respect to the energy-constrained diamond norms, which imply uniform continuity of these characteristics with respect to the strong convergence topology.

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English version:
Problems of Information Transmission, 2018, 54:1, 20–33

Bibliographic databases:

Document Type: Article
UDC: 621.391.1+519.72
Received: 08.08.2017
Revised: 14.12.2017

Citation: M. E. Shirokov, “On the energy-constrained diamond norm and its application in quantum information theory”, Probl. Peredachi Inf., 54:1 (2018), 24–38; Problems Inform. Transmission, 54:1 (2018), 20–33

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