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Additivity/Multiplicativity Communication Channels

  • G. G. Amosov
  • A. S. Holevo
  • R. F. Werner

Abstract

A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the “classical capacity”, and the “maximal output purity”. All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.

Keywords

Tensor Product Quantum Channel Quantum Communication Classical Communication Quantum Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    C. H. Bennett, P. W. Shor, Quantum information theory, IEEE Trans. on Inform. Theory, IT–44, 2724–2742, 1998.MathSciNetCrossRefGoogle Scholar
  2. [2]
    C. H. Bennett, C. Fuchs, J. A. Smolin, Entanglement enhanced classical communication on a noisy quantum channel, in: Proc. 3d Int. Conf. on Quantum Communication and Measurement, ed. by C. M. Caves, O. Hirota, A. S. Holevo, Plenum, NY 1997. LANL e-print quant-ph/9611006.Google Scholar
  3. [3]
    A. S. Holevo, Quantum coding theorems, Russian Math. Surveys 53:6, 1295–1331, 1998. LANL e-print quant-ph/9808023.CrossRefzbMATHMathSciNetADSGoogle Scholar
  4. [4]
    G. Lindblad, Quantum entropy and quantum measurements, in: Proc. Int. Conf. on Quantum Communication and Measurement, ed. by C. Benjaballah, O. Hirota, S. Reynaud, Lect. Notes Phys. 378, 71–80, Springer-Verlag, Berlin 1991.Google Scholar
  5. [5]
    B. Schumacher, M. D. Westmoreland, Optimal signal ensembles. LANL e-print quant-ph/9912122.Google Scholar
  6. [6]
    C. Fuchs, private communication.Google Scholar
  7. [7]
    C. King, M. B. Ruskai, Minimal entropy of states emerging from noisy quantum channels. LANL e-print quant-ph/9911079.Google Scholar
  8. [8]
    D. Brass, L. Faoro, C. Macchiavello, M. Palma, Quantum entanglement and classical communication through a depolarizing channel. J. Mod. Opt. 47, 325–332, 2000. LANL e-print quant-ph/9903033.ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • G. G. Amosov
    • 1
  • A. S. Holevo
    • 2
  • R. F. Werner
    • 3
  1. 1.Moscow Institute for Physics and TechnologyMoscowRussia
  2. 2.Steklov Mathematical InstituteMoscow
  3. 3.Institut für Mathematische PhysikTU BraunschweigBraunschweigGermany

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