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Communications in Mathematical Physics

, Volume 260, Issue 3, pp 659–671 | Cite as

A Quantum Version of Sanov's Theorem

  • Igor BjelakovićEmail author
  • Jean-Dominique Deuschel
  • Tyll Krüger
  • Ruedi Seiler
  • Rainer Siegmund-Schultze
  • Arleta Szkoła
Article

Abstract

We present a quantum version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set Ψ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the separating rate on a logarithmic scale is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set Ψ. While in the classical case the separating subsets can be chosen universally, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.

Keywords

Entropy Stationary Quantum Reference State Quantum Computing Logarithmic Scale 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor Bjelaković
    • 1
    Email author
  • Jean-Dominique Deuschel
    • 1
  • Tyll Krüger
    • 1
    • 2
  • Ruedi Seiler
    • 1
  • Rainer Siegmund-Schultze
    • 1
    • 3
  • Arleta Szkoła
    • 1
    • 4
  1. 1.Institut für Mathematik MA 7-2Technische Universität Berlin, Fakultät II - Mathematik und NaturwissenschaftenBerlinGermany
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  3. 3.Institut für MathematikTechnische Universität IlmenauIlmenauGermany
  4. 4.Max Planck Institute for Mathematics in the Sciences LeipzigGermany

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