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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 2(368), Pages 113–152 (Mi umn1709)  

This article is cited in 12 scientific papers (total in 12 papers)

Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The additivity problem is one of the most profound mathematical problems of quantum information theory. From an analytical point of view it is closely related to the multiplicative property, with respect to tensor products, of norms of maps on operator spaces equipped with the Schatten norms (non-commutative analogue of $l_p$-norms). In this paper we survey the current state of the problem.


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English version:
Russian Mathematical Surveys, 2006, 61:2, 301–339

Bibliographic databases:

Document Type: Article
UDC: 519.248.3
MSC: Primary 94A40, 81P68; Secondary 94A17, 47B10, 47B65
Received: 12.01.2006

Citation: A. S. Holevo, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Uspekhi Mat. Nauk, 61:2(368) (2006), 113–152; Russian Math. Surveys, 61:2 (2006), 301–339

Citation in format AMSBIB
\by A.~S.~Holevo
\paper Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory
\jour Uspekhi Mat. Nauk
\yr 2006
\vol 61
\issue 2(368)
\pages 113--152
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 2
\pages 301--339

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    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. Szarek S.J., “On Norms of Completely Positive Maps”, Topics in Operator Theory: Operators, Matrices and Analytic Functions, Operator Theory Advances and Applications, 1, 2010, 535–538  mathscinet  isi
    3. M.M.. Wilde, Andreas Winter, Dong Yang, “Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy”, Commun. Math. Phys, 2014  crossref  mathscinet  isi  scopus
    4. 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
    5. Winter A., “Weak Locking Capacity of Quantum Channels Can be Much Larger Than Private Capacity”, J. Cryptology, 30:1 (2017), 1–21  crossref  mathscinet  zmath  isi  scopus
    6. Kaur E., Wilde M.M., “Relative Entropy of Steering: on Its Definition and Properties”, J. Phys. A-Math. Theor., 50:46 (2017), 465301  crossref  mathscinet  zmath  isi  scopus
    7. De Palma G., Trevisan D., Giovannetti V., “Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels”, Phys. Rev. Lett., 118:16 (2017), 160503  crossref  mathscinet  isi  scopus
    8. Kaur E., Wilde M.M., “Amortized Entanglement of a Quantum Channel and Approximately Teleportation-Simulable Channels”, J. Phys. A-Math. Theor., 51:3 (2018), 035303  crossref  mathscinet  zmath  isi  scopus
    9. De Palma G., “The Wehrl Entropy Has Gaussian Optimizers”, Lett. Math. Phys., 108:1 (2018), 97–116  crossref  mathscinet  zmath  isi  scopus
    10. D. Ding, M. M. Wilde, “Strong converse for the feedback-assisted classical capacity of entanglement-breaking channels”, Problems Inform. Transmission, 54:1 (2018), 1–19  mathnet  crossref  isi  elib
    11. De Palma G., Trevisan D., Giovannetti V., “The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussianmaximizers”, Ann. Henri Poincare, 19:10 (2018), 2919–2953  crossref  mathscinet  zmath  isi  scopus
    12. De Palma G., Trevisan D., Giovannetti V., Ambrosio L., “Gaussian Optimizers For Entropic Inequalities in Quantum Information”, J. Math. Phys., 59:8 (2018), 081101  crossref  mathscinet  zmath  isi  scopus
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