Year: 2018
Type: article
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.
Author: M. E. Shirokov
Institutions: Russian Academy of Sciences, Steklov Mathematical Institute
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2620699733