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Russian Mathematical Surveys, 2006, Volume 61, Issue 2, Pages 301–339
DOI: https://doi.org/10.1070/RM2006v061n02ABEH004313 (Mi rm1709) 		 
This article is cited in 18 scientific papers (total in 18 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
English version PDF (531 kB) Citations (18)
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DOI: https://doi.org/10.1070/RM2006v061n02ABEH004313
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.
Received: 12.01.2006
Russian version:
Uspekhi Matematicheskikh Nauk, 2006, Volume 61, Issue 2(368), Pages 113–152
DOI: https://doi.org/10.4213/rm1709
Bibliographic databases:
Document Type: Article
UDC: 519.248.3
MSC: Primary 94A40, 81P68; Secondary 94A17, 47B10, 47B65
Language: English
Original paper language: Russian
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
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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