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

This article is cited in 9 scientific papers (total in 9 papers)

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
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

Citation in format AMSBIB
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\pages 20--33
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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  crossref  mathscinet  zmath  isi  scopus
    2. Nair R., “Quantum-Limited Loss Sensing: Multiparameter Estimation and Bures Distance Between Loss Channels”, Phys. Rev. Lett., 121:23 (2018), 230801  crossref  isi  scopus
    3. Shirokov M.E., “Uniform Finite-Dimensional Approximation of Basic Capacities of Energy-Constrained Channels”, Quantum Inf. Process., 17:12 (2018), UNSP 322  crossref  mathscinet  isi  scopus
    4. Lami L. Sabapathy K.K. Winter A., “All Phase-Space Linear Bosonic Channels Are Approximately Gaussian Dilatable”, New J. Phys., 20 (2018), 113012  crossref  isi  scopus
    5. Wilde M.M., “Entanglement Cost and Quantum Channel Simulation”, Phys. Rev. A, 98:4 (2018), 042338  crossref  mathscinet  isi  scopus
    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  crossref  mathscinet  isi  scopus
    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  crossref  mathscinet  isi  scopus
    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  crossref  isi  scopus
    9. Wilde M.M., “Strong and Uniform Convergence in the Teleportation Simulation of Bosonic Gaussian Channels”, Phys. Rev. A, 97:6 (2018), 062305  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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