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Annales Henri Poincaré

, Volume 2, Issue 1, pp 1–26 | Cite as

The Rate of Optimal Purification Procedures

  • M. Keyl
  • R.F. Werner

Abstract.

Purification is a process in which decoherence is partially reversed by using several input systems which have been subject to the same noise. The purity of the outputs generally increases with the number of input systems, and decreases with the number of required output systems. We construct the optimal quantum operations for this task, and discuss their asymptotic behaviour as the number of inputs goes to infinity. The rate at which output systems may be generated depends crucially on the type of purity requirement. If one tests the purity of the output systems one at a time, the rate is infinite: this fidelity may be made to approach 1, while at the same time the number of outputs goes to infinity arbitrarily fast. On the other hand, if one also requires the correlations between outputs to decrease, the rate is zero: if fidelity with the pure product state is to go to 1, the number of outputs per input goes to zero. However, if only a fidelity close to 1 is required, the optimal purifier achieves a positive rate, which we compute.

Keywords

Asymptotic Behaviour Product State Output System Purification Procedure Pure Product 
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

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • M. Keyl
    • 1
  • R.F. Werner
    • 2
  1. 1.Institut für Mathematische Physik, TU Braunschweig, Mendeslssohnstrasse 3, D-38106 Braunschweig, Germany, e-mail: m.keyl@tu-bs.deDE
  2. 2.Institut für Mathematische Physik, TU Braunschweig, Mendeslssohnstrasse 3, D-38106 Braunschweig, Germany, e-mail: R.Werner@tu-bs.deDE

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