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TMF, 2015, Volume 182, Number 2, Pages 338–349 (Mi tmf8777)  

This article is cited in 15 scientific papers (total in 15 papers)

Majorization and additivity for multimode bosonic Gaussian channels

V. Giovannettia, A. S. Holevob, A. Maria

a NEST, Scuola Normale Superiore e Istituto Nanoscienze CNR, Pisa, Italy
b Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We obtain a multimode extension of the majorization theorem for bosonic Gaussian channels, in particular, giving sufficient conditions under which the Glauber coherent states are the only minimizers for concave functionals of the output state of such a channel. We discuss direct implications of this multimode majorization for the positive solution of the famous additivity problem in the case of Gaussian channels. In particular, we prove the additivity of the output Rényi entropies of arbitrary order $p>1$. Finally, we present an alternative, more direct derivation of a majorization property of the Husimi function established by Lieb and Solovej.

Keywords: quantum information theory, bosonic Gaussian communication channel, classical capacity, gauge invariance, minimal output entropy, Gaussian optimizer, additivity

Funding Agency Grant Number
Russian Science Foundation 14-21-00162


DOI: https://doi.org/10.4213/tmf8777

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2015, 182:2, 284–293

Bibliographic databases:

Received: 11.08.2014

Citation: V. Giovannetti, A. S. Holevo, A. Mari, “Majorization and additivity for multimode bosonic Gaussian channels”, TMF, 182:2 (2015), 338–349; Theoret. and Math. Phys., 182:2 (2015), 284–293

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. A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. G. De Palma, A. Mari, S. Lloyd, V. Giovannetti,, “Multimode quantum entropy power inequality”, Phys. Rev. A, 91:3 (2015), 032320  crossref  adsnasa  isi  scopus
    3. K. K. Sabapathy, “Quantum-optical channels that output only classical states”, Phys. Rev. A, 92:5 (2015), 052301  crossref  adsnasa  isi  elib  scopus
    4. M. Rosati, A. Mari, V. Giovannetti, “Multiphase Hadamard receivers for classical communication on lossy bosonic channels”, Phys. Rev. A, 94:6 (2016), 062325  crossref  isi  elib  scopus
    5. G. De Palma, A. Mari, S. Lloyd, V. Giovannetti, “Passive states as optimal inputs for single-jump lossy quantum channels”, Phys. Rev. A, 93:6 (2016), 062328  crossref  isi  scopus
    6. G. De Palma, D. Trevisan, V. Giovannetti, “Passive states optimize the output of bosonic Gaussian quantum channels”, IEEE Trans. Inf. Theory, 62:5 (2016), 2895–2906  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. G. De Palma, D. Trevisan, V. Giovannetti, “Gaussian states minimize the output entropy of one-mode quantum Gaussian channels”, Phys. Rev. Lett., 118:16 (2017), 160503  crossref  mathscinet  isi  scopus
    9. M. Rosati, A. Mari, V. Giovannetti, “Capacity of coherent-state adaptive decoders with interferometry and single-mode detectors”, Phys. Rev. A, 96:1 (2017), 012317  crossref  isi  scopus
    10. G. De Palma, “The Wehrl entropy has Gaussian optimizers”, Lett. Math. Phys., 108:1 (2018), 97–116  crossref  mathscinet  zmath  isi  scopus
    11. G. De Palma, D. Trevisan, V. Giovannetti, “The one-mode quantum-limited Gaussian attenuator and amplifier have Gaussian maximizers”, Ann. Henri Poincare, 19:10 (2018), 2919–2953  crossref  mathscinet  zmath  isi  scopus
    12. G. De Palma, D. Trevisan, V. Giovannetti, L. Ambrosio, “Gaussian optimizers for entropic inequalities in quantum information”, J. Math. Phys., 59:8 (2018), 081101  crossref  mathscinet  zmath  isi  scopus
    13. M. M. Wilde, “Entanglement cost and quantum channel simulation”, Phys. Rev. A, 98:4 (2018), 042338  crossref  mathscinet  isi  scopus
    14. Jabbou M.G., Cerf N.J., “Fock Majorization in Bosonic Quantum Channels With a Passive Environment”, J. Phys. A-Math. Theor., 52:10 (2019), 105302  crossref  isi  scopus
    15. Quantum Electron., 50:5 (2020), 440–446  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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