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TMF, 2011, Volume 166, Number 1, Pages 142–159 (Mi tmf6601)  

This article is cited in 20 scientific papers (total in 20 papers)

Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions

A. S. Holevo

Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We consider the entropy gain for infinite-dimensional evolutions and show that unlike in the finite-dimensional case, there are many channels with positive minimal entropy gain. We obtain a new lower bound and compute the minimal entropy gain for a broad class of bosonic Gaussian channels. We mathematically formulate the Choi–Jamiolkowski (CJ) correspondence between channels and states in the infinite-dimensional case in a form close to the form used in quantum information theory. In particular, we obtain an explicit expression for the CJ operator defining a general nondegenerate bosonic Gaussian channel and compute its norm.

Keywords: quantum entropy, completely positive map, Choi–Jamiolkowski correspondence, bosonic Gaussian channel

DOI: https://doi.org/10.4213/tmf6601

Full text: PDF file (519 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:1, 123–138

Bibliographic databases:

Received: 17.05.2010

Citation: A. S. Holevo, “Entropy gain and the Choi–Jamiolkowski correspondence for infinite-dimensional quantum evolutions”, TMF, 166:1 (2011), 142–159; Theoret. and Math. Phys., 166:1 (2011), 123–138

Citation in format AMSBIB
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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. Holevo A.S., “The Choi-Jamiolkowski forms of quantum Gaussian channels”, J Math Phys, 52:4 (2011), 042202  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14  mathnet  crossref  mathscinet  isi
    3. Majewski W.A., “On Positive Maps in Quantum Information”, Russ. J. Math. Phys., 21:3 (2014), 362–372  crossref  mathscinet  zmath  isi  scopus
    4. Sun X.-H., Li Yu., “Some Characterizations of Quantum Channel in Infinite Hilbert Spaces”, J. Math. Phys., 55:5 (2014), 053511  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Hansen F., “Trace Functions With Applications in Quantum Physics”, J. Stat. Phys., 154:3 (2014), 807–818  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Stormer E., “The Analogue of Choi Matrices For a Class of Linear Maps on Von Neumann Algebras”, Int. J. Math., 26:2 (2015), 1550018  crossref  mathscinet  zmath  isi  scopus
    7. Alazzawi S., Baumgartner B., “Generalized Kraus Operators and Generators of Quantum Dynamical Semigroups”, Rev. Math. Phys., 27:7 (2015), 1550016  crossref  mathscinet  zmath  isi  elib  scopus
    8. Giacomini F., Castro-Ruiz E., Brukner C., “Indefinite causal structures for continuous-variable systems”, New J. Phys., 18 (2016), 113026  crossref  isi  elib  scopus
    9. Buscemi F., Das S., Wilde M.M., “Approximate reversibility in the context of entropy gain, information gain, and complete positivity”, Phys. Rev. A, 93:6 (2016), 062314  crossref  mathscinet  isi  elib  scopus
    10. Fiedler L., Naaijkens P., Osborne T.J., “Jones index, secret sharing and total quantum dimension”, New J. Phys., 19 (2017), 023039  crossref  isi  scopus
    11. A. S. Holevo, “On the quantum Gaussian optimizers conjecture in the case $q=p$”, Russian Math. Surveys, 72:6 (2017), 1177–1179  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Li Yu., “Complete Order Structures For Completely Bounded Maps Involving Trace Class Operators”, Houst. J. Math., 43:4 (2017), 1165–1185  mathscinet  zmath  isi
    13. Frank R.L., Lieb E.H., “Norms of Quantum Gaussian Multi-Mode Channels”, J. Math. Phys., 58:6 (2017), 062204  crossref  mathscinet  zmath  isi  scopus
    14. Lami L., Das S., Wilde M.M., “Approximate Reversal of Quantum Gaussian Dynamics”, J. Phys. A-Math. Theor., 51:12 (2018), 125301  crossref  mathscinet  zmath  isi  scopus
    15. 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
    16. Seshadreesan K.P., Lami L., Wilde M.M., “Renyi Relative Entropies of Quantum Gaussian States”, J. Math. Phys., 59:7 (2018), 072204  crossref  mathscinet  zmath  isi  scopus
    17. Zhuang Q., Zhang Zh., Lutkenhaus N., Shapiro J.H., “Security-Proof Framework For Two-Way Gaussian Quantum-Key-Distribution Protocols”, Phys. Rev. A, 98:3 (2018), 032332  crossref  isi  scopus
    18. Kuramochi Yu., “Entanglement-Breaking Channels With General Outcome Operator Algebras”, J. Math. Phys., 59:10 (2018), 102206  crossref  mathscinet  zmath  isi  scopus
    19. Faist Ph., Berta M., Brandao F., “Thermodynamic Capacity of Quantum Processes”, Phys. Rev. Lett., 122:20 (2019), 200601  crossref  isi
    20. Friedland Sh., “Infinite Dimensional Generalizations of Choi'S Theorem”, Spec. Matrices, 7:1 (2019), 67–77  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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