Generalized Quantum Dynamics

  • János A. Bergou
  • Mark Hillery
Part of the Graduate Texts in Physics book series (GTP)


Time evolution in textbook quantum mechanics is represented by unitary maps \(\vert \psi \rangle \rightarrow U\vert \psi \rangle\) and \(\rho \rightarrow U\rho {U}^{\dag }\), where \(U ={ \mathrm{e}}^{-itH}\). This is not the most general evolution possible. We can couple our system to another one, evolve both with a unitary operator that will, in general, create entanglement between the two systems, and then trace out the second system. The resulting evolution for the original system alone will be non-unitary, in general, and can be described by a non-unitary quantum map.


Generalized Quantum Dynamics Quantum Map Quantum Mechanics Textbooks Kraus Representation Kraus Operators 
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    J. Preskill, Lecture Notes for Physics 219
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    W.K. Wooters, W.H. Zurek, A single quantum cannot be cloned. Nature 299, 802 (1982)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • János A. Bergou
    • 1
  • Mark Hillery
    • 1
  1. 1.Department of Physics and AstronomyHunter College City University of New YorkNew YorkUSA

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