RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 1, Pages 133–143 (Mi tvp151)  

This article is cited in 41 scientific papers (total in 41 papers)

Complementary channels and the additivity problem

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We explore the complementarity between output and environment of a quantum channel (or, more generally, completely positive (CP) map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, the validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement-breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in a new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.

Keywords: quantum channel, completely positive map, additivity conjecture.

DOI: https://doi.org/10.4213/tvp151

Full text: PDF file (1369 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2007, 51:1, 92–100

Bibliographic databases:

Document Type: Article
Received: 07.10.2005

Citation: A. S. Holevo, “Complementary channels and the additivity problem”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 133–143; Theory Probab. Appl., 51:1 (2007), 92–100

Citation in format AMSBIB
\Bibitem{Hol06}
\by A.~S.~Holevo
\paper Complementary channels and the additivity problem
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 1
\pages 133--143
\mathnet{http://mi.mathnet.ru/tvp151}
\crossref{https://doi.org/10.4213/tvp151}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2324171}
\zmath{https://zbmath.org/?q=an:1113.81022}
\elib{http://elibrary.ru/item.asp?id=9233594}
\transl
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 1
\pages 92--100
\crossref{https://doi.org/10.1137/S0040585X97982244}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000245677000006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247481757}


Linking options:
  • http://mi.mathnet.ru/eng/tvp151
  • https://doi.org/10.4213/tvp151
  • http://mi.mathnet.ru/eng/tvp/v51/i1/p133

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. M. E. Shirokov, “Superadditivity of the convex closure of the output entropy of a quantum channel”, Russian Math. Surveys, 61:6 (2006), 1186–1188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. S. Holevo, “Single-Mode Quantum Gaussian Channels: Structure and Quantum Capacity”, Problems Inform. Transmission, 43:1 (2007), 1–11  mathnet  crossref  mathscinet  isi
    3. Caruso F., Giovannetti V., “Qubit quantum channels: A characteristic function approach”, Phys. Rev. A, 76:4 (2007), 042331, 10 pp.  crossref  adsnasa  isi  elib  scopus
    4. Buscemi F., “Channel correction via quantum erasure”, Phys. Rev. Lett., 99:18 (2007), 180501, 4 pp.  crossref  adsnasa  isi  scopus
    5. M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90  mathnet  crossref  mathscinet  isi  elib
    6. Cubitt T.S., Ruskai M.B., Smith G., “The structure of degradable quantum channels”, J. Math. Phys., 49:10 (2008), 102104, 27 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Kretschmann D., Kribs D.W., Spekkens R.W., “Complementarity of private and correctable subsystems in quantum cryptography and error correction”, Phys. Rev. A, 78:3 (2008), 032330, 5 pp.  crossref  adsnasa  isi  scopus
    8. Caruso F., Eisert J., Giovannetti V., Holevo A.S., “Multi–mode bosonic Gaussian channels”, New J. Phys., 10 (2008), 083030, 33 pp.  crossref  isi  elib  scopus
    9. Rybár T., Ziman M., “Quantum finite–depth memory channels: Case study”, Phys. Rev. A, 80:4 (2009), 042306, 7 pp.  crossref  adsnasa  isi  elib  scopus
    10. Fukuda M., “An application of decomposable maps in proving multiplicativity of low dimensional maps”, J. Math. Phys., 51:2 (2010), 022201, 7 pp.  crossref  zmath  adsnasa  isi  scopus
    11. A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218  mathnet  crossref  mathscinet  isi
    12. Rosgen B., “Computational distinguishability of degradable and antidegradable channels”, Quantum Inf. Comput., 10:9-10 (2010), 735–746  mathscinet  zmath  isi  elib
    13. Fukuda M., King Ch., “Entanglement of random subspaces via the Hastings bound”, J. Math. Phys., 51:4 (2010), 042201, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Huang P., He G., Lu Yu., Zeng G., “Quantum capacity of Pauli channels with memory”, Phys. Scripta, 83:1 (2011), 015005  crossref  zmath  adsnasa  isi  elib  scopus
    15. M. E. Shirokov, “The continuity of the output entropy of positive maps”, Sb. Math., 202:10 (2011), 1537–1564  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. Brádler K., “Further discussion on capacities of the Unruh and Grassmann channel”, Revista Mexicana de Física, 57, Suppl. S:3 (2011), 79–84  isi
    17. Brádler K., “An infinite sequence of additive channels: the classical capacity of cloning channels”, IEEE Trans. Inform. Theory, 57:8 (2011), 5497–5503  crossref  mathscinet  zmath  isi  elib  scopus
    18. A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10  mathnet  crossref  isi
    19. Fischmann J., Bruzda W., Khoruzhenko B.A., Sommers H.-J., Życzkowski K., “Induced Ginibre ensemble of random matrices and quantum operations”, J. Phys. A, 45:7 (2012), 075203, 31 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. M. E. Shirokov, “Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel”, Problems Inform. Transmission, 48:2 (2012), 85–101  mathnet  crossref  isi
    21. Collins B., Fukuda M., Nechita I., “Towards a State Minimizing the Output Entropy of a Tensor Product of Random Quantum Channels”, J. Math. Phys., 53:3 (2012), 032203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. A. S. Holevo, “Extreme bosonic linear channels”, Theoret. and Math. Phys., 174:2 (2013), 288–297  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. M. E. Shirokov, “Reversibility conditions for quantum channels and their applications”, Sb. Math., 204:8 (2013), 1215–1237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31  mathnet  crossref  isi
    25. G. G. Amosov, “On estimating the output entropy of the tensor product of a phase-damping channel and an arbitrary channel”, Problems Inform. Transmission, 49:3 (2013), 224–231  mathnet  crossref  isi  elib
    26. M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Sb. Math., 205:7 (2014), 1045–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. M. E. Shirokov, T. V. Shulman, “On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements”, Problems Inform. Transmission, 50:3 (2014), 232–246  mathnet  crossref  mathscinet  isi
    28. Caruso F., Giovannetti V., Lupo C., Mancini S., “Quantum Channels and Memory Effects”, Rev. Mod. Phys., 86:4 (2014), 1203–1259  crossref  adsnasa  isi  scopus
    29. Giovannetti V., Garcia-Patron R., Cerf N.J., Holevo A.S., “Ultimate Classical Communication Rates of Quantum Optical Channels”, Nat. Photonics, 8:10 (2014), 796–800  crossref  adsnasa  isi  scopus
    30. Al Nuwairan M., “The Extreme Points of $\mathrm{SU}(2)$-Irreducibly Covariant Channels”, Int. J. Math., 25:6 (2014), 1450048  crossref  mathscinet  zmath  isi  scopus
    31. Bennett Ch.H., Devetak I., Harrow A.W., Shor P.W., Winter A., “The Quantum Reverse Shannon Theorem and Resource Tradeoffs For Simulating Quantum Channels”, IEEE Trans. Inf. Theory, 60:5 (2014), 2926–2959  crossref  mathscinet  zmath  isi  elib  scopus
    32. G. G. Amosov, “Estimating the output entropy of a tensor product of two quantum channels”, Theoret. and Math. Phys., 182:3 (2015), 397–406  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    33. 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
    34. G. G. Amosov, I. Yu. Zhdanovskii, “Structure of the Algebra Generated by a Noncommutative Operator Graph which Demonstrates the Superactivation Phenomenon for Zero-Error Capacity”, Math. Notes, 99:6 (2016), 924–927  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    35. Fukuda M. Gour G., “Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula”, IEEE Trans. Inf. Theory, 63:3 (2017), 1818–1828  crossref  mathscinet  zmath  isi  scopus
    36. Zhuang Q., Zhu E.Y., Shor P.W., “Additive Classical Capacity of Quantum Channels Assisted By Noisy Entanglement”, Phys. Rev. Lett., 118:20 (2017), 200503  crossref  mathscinet  isi  scopus
    37. Kuramochi Yu., “Quantum Incompatibility of Channels With General Outcome Operator Algebras”, J. Math. Phys., 59:4 (2018), 042203  crossref  mathscinet  zmath  isi  scopus
    38. Mukhamedov F., Watanabe N., “On S-Mixing Entropy of Quantum Channels”, Quantum Inf. Process., 17:6 (2018), UNSP 148  crossref  mathscinet  isi  scopus
    39. Davis N., Shirokov M.E., Wilde M.M., “Energy-Constrained Two-Way Assisted Private and Quantum Capacities of Quantum Channels”, Phys. Rev. A, 97:6 (2018), 062310  crossref  mathscinet  isi  scopus
    40. Shirokov M.E., “Uniform Continuity Bounds For Information Characteristics of Quantum Channels Depending on Input Dimension and on Input Energy”, J. Phys. A-Math. Theor., 52:1 (2019), 014001  crossref  mathscinet  isi  scopus
    41. Kribs D.W., Pereira R., Levick J., Rahaman M., Nelson I M., “Quantum Complimentarity and Operator Structures”, Quantum Inform. Comput., 19:1-2 (2019), 67–83  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:661
    Full text:22
    References:48

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019