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Phys. Rev. Lett. 103, 210401 (2009) [4 pages]

Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems

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Heinz-Peter Breuer1,*, Elsi-Mari Laine2, and Jyrki Piilo2,†
1Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
2Turku Center for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland

Received 31 July 2009; revised 12 October 2009; published 16 November 2009

See accompanying Physics Synopsis

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.103.210401
DOI:
10.1103/PhysRevLett.103.210401
PACS:
03.65.Yz, 03.65.Ta, 42.50.Lc

*breuer@physik.uni-freiburg.de

jyrki.piilo@utu.fi