Applied Physics B

, Volume 86, Issue 3, pp 371–375 | Cite as

Purifying and reversible physical processes

  • M. KleinmannEmail author
  • H. Kampermann
  • T. Meyer
  • D. Bruß


Starting from the observation that reversible processes cannot increase the purity of any input state, we study deterministic physical processes, which map a set of states to a set of pure states. Such a process must map any state to the same pure output, if purity is demanded for the input set of all states. But otherwise, when the input set is restricted, it is possible to find non-trivial purifying processes. For the most restricted case of only two input states, we completely characterise the output of any such map. We furthermore consider maps, which combine the property of purity and reversibility on a set of states, and we derive necessary and sufficient conditions on sets, which permit such processes.


Pure State Success Probability Input State Kraus Operator Trace Distance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Forrest Stinespring, Proc. Am. Math. Soc. 6, 211 (1955)zbMATHCrossRefGoogle Scholar
  2. 2.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (University Press, Cambridge, 2000)zbMATHGoogle Scholar
  3. 3.
    K. Kraus, States, Effects and Operations (Springer, Berlin, 1983)zbMATHGoogle Scholar
  4. 4.
    M. Kleinmann, H. Kampermann, T. Meyer, D. Bruß, Phys. Rev. A 73, 062309 (2006)CrossRefADSGoogle Scholar
  5. 5.
    G.W. Stewart, J.G. Sun, Matrix Pertubation Theory (Academic, San Diego, 1990)Google Scholar
  6. 6.
    C.W. Helstrøm, Quantum Detection and Estimation Theory (Academic, New York, 1976)Google Scholar
  7. 7.
    U. Herzog, J.A. Bergou, Phys. Rev. A 70, 022302 (2004)CrossRefADSGoogle Scholar
  8. 8.
    T. Rudolph, R.W. Spekkens, P.S. Turner, Phys. Rev. A 68, 010301 (2003)CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    L.P. Hughston, R. Jozsa, W.K. Wootters, Phys. Lett. A 183, 14 (1993)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    A. Bassi, G.C. Ghirardi, Phys. Lett. A 309, 24 (2003)zbMATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    G. Jaeger, A. Shimony, Phys. Lett. A 197, 83 (1995)zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Y. Feng, R. Duan, Y. Mingsheng, Phys. Rev. A 70, 012308 (2004)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • M. Kleinmann
    • 1
    Email author
  • H. Kampermann
    • 1
  • T. Meyer
    • 1
  • D. Bruß
    • 1
  1. 1.Institut für Theoretische PhysikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

Personalised recommendations