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An application of decomposable maps in proving multiplicativity of low dimensional maps

Source: J. Math. Phys. 51, 022201 (2010); doi:10.1063/1.3277186

Published 2 February 2010 | See: Publisher's Note

ERRATUM
  1. Publisher's Note: “An application of decomposable maps in proving multiplicativity of low dimensional maps” [J. Math. Phys. 51, 022201 (2010)]
    Motohisa Fukuda
    J. Math. Phys. 51, 029902 (2010)
KEYWORDS and PACS
Keywords
PACS
  • 03.67.-a
    Quantum information
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • YEAR: 2010
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Motohisa Fukuda
Department of Mathematics, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
In this paper, we present a class of maps for which the multiplicativity of the maximal output p-norm holds for p=2 and p>=4. The class includes all positive trace-preserving maps from [script B]([openface C]3) to [script B]([openface C]2). In this sense, the result is a generalization of the corresponding result in the work of King and Koldan [“New multiplicativity results for qubit maps,” J. Math. Phys. 47, 042106 (2006)], where the multiplicativity was proved for all positive trace-preserving maps from [script B]([openface C]2) to [script B]([openface C]2) with p=2 and p>=4. Interestingly, by contrast, the multiplicativity of p-norm was investigated in the context of quantum information theory and shown not to hold, in general, for high dimensional quantum channels [Hayden, P. and Winter, A., “Counterexamples to the maximal p-norm multiplicativity conjecture for all p>1,” Commun. Math. Phys. 284, 263 (2008)]. Moreover, the Werner–Holevo channel, which is a map from [script B]([openface C]3) to [script B]([openface C]3), is a counterexample for p>4.79 [Werner and Holevo, J. Math. Phys. 43, 4353 (2002).]. ©2010 American Institute of Physics
History: Received 20 June 2009; accepted 3 December 2009; published 2 February 2010; corrected 8 February 2010
Permalink: http://link.aip.org/link/?JMAPAQ/51/022201/1

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