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Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 2, pp. 301-339 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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A. S. Holevo. Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 2, pp. 301-339. http://geodesic.mathdoc.fr/item/RM_2006_61_2_a2/

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