2017/06/01 by M. E. Shirokov · 1 voice · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Quantum Information and Cryptography #Quantum Mechanics and Applications #math-ph #quant-ph
paper · pdf · doi:10.1134/s0032946018010027
arxiv published 2017/06/01 · openalex created_date 2017/06/09 · arxiv updated 2017/06/23 · openalex publication_date 2018/01/01 · openalex updated_date 2026/07/31
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.