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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:

UDC: 621.391.1+519.72
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

Citation in format AMSBIB
\Bibitem{Shi18} \by M.~E.~Shirokov \paper On the energy-constrained diamond norm and its application in quantum information theory \jour Probl. Peredachi Inf. \yr 2018 \vol 54 \issue 1 \pages 24--38 \mathnet{http://mi.mathnet.ru/ppi2257} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3799305} \elib{http://elibrary.ru/item.asp?id=32614061} \transl \jour Problems Inform. Transmission \yr 2018 \vol 54 \issue 1 \pages 20--33 \crossref{https://doi.org/10.1134/S0032946018010027} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000429943100002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045532761} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Cope T.P.W., Goodenough K., Pirandola S., “Converse Bounds For Quantum and Private Communication Over Holevo-Werner Channels”, J. Phys. A-Math. Theor., 51:49 (2018), 494001
2. Nair R., “Quantum-Limited Loss Sensing: Multiparameter Estimation and Bures Distance Between Loss Channels”, Phys. Rev. Lett., 121:23 (2018), 230801
3. Shirokov M.E., “Uniform Finite-Dimensional Approximation of Basic Capacities of Energy-Constrained Channels”, Quantum Inf. Process., 17:12 (2018), UNSP 322
4. Lami L. Sabapathy K.K. Winter A., “All Phase-Space Linear Bosonic Channels Are Approximately Gaussian Dilatable”, New J. Phys., 20 (2018), 113012
5. Wilde M.M., “Entanglement Cost and Quantum Channel Simulation”, Phys. Rev. A, 98:4 (2018), 042338
6. Knott P.A., Tufarelli T., Piani M., Adesso G., “Generic Emergence of Objectivity of Observables in Infinite Dimensions”, Phys. Rev. Lett., 121:16 (2018), 160401
7. Pirandola S. Braunstein S.L. Laurenza R. Ottaviani C. Cope T.P.W. Spedalieri G. Banchi L., “Theory of Channel Simulation and Bounds For Private Communication”, Quantum Sci. Technol., 3:3 (2018), UNSP 035009
8. Sharma K. Wilde M.M. Adhikari S. Takeoka M., “Bounding the Energy-Constrained Quantum and Private Capacities of Phase-Insensitive Bosonic Gaussian Channels”, New J. Phys., 20 (2018), 063025
9. Wilde M.M., “Strong and Uniform Convergence in the Teleportation Simulation of Bosonic Gaussian Channels”, Phys. Rev. A, 97:6 (2018), 062305
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