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Phys. Rev. A 71, 020101(R) (2005) [4 pages]

Completely positive post-Markovian master equation via a measurement approach

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A. Shabani1 and D. A. Lidar2
1Physics Department and Center for Quantum Information and Quantum Control, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7
2Chemical Physics Theory Group, Chemistry Department, and Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George St., Toronto, Ontario, Canada M5S 3H6

Received 12 April 2004; revised 19 October 2004; published 15 February 2005

A post-Markovian quantum master equation is derived, which includes bath memory effects via a phenomenologically introduced memory kernel k(t). The derivation uses as a formal tool a probabilistic single-shot bath-measurement process performed during the coupled system-bath evolution. The resulting analytically solvable master equation interpolates between the exact Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and sufficient condition for complete positivity in terms of properties of k(t) is presented, in addition to a prescription for the experimental determination of k(t). The formalism is illustrated with examples.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.71.020101
DOI:
10.1103/PhysRevA.71.020101
PACS:
03.65.Yz, 03.67.−a, 42.50.Lc
 
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