Completely positive post-Markovian master equation via a measurement approach
Abstract
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.
- Authors:
-
- Physics Department and Center for Quantum Information and Quantum Control, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7 (Canada)
- Chemical Physics Theory Group, Chemistry Department, and Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George St., Toronto, Ontario, M5S 3H6 (Canada)
- Publication Date:
- OSTI Identifier:
- 20650022
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. A
- Additional Journal Information:
- Journal Volume: 71; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.71.020101; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; EQUATIONS; EVOLUTION; KERNELS; MARKOV PROCESS; PROBABILISTIC ESTIMATION; QUANTUM MECHANICS
Citation Formats
Shabani, A, and Lidar, D A. Completely positive post-Markovian master equation via a measurement approach. United States: N. p., 2005.
Web. doi:10.1103/PhysRevA.71.020101.
Shabani, A, & Lidar, D A. Completely positive post-Markovian master equation via a measurement approach. United States. https://doi.org/10.1103/PhysRevA.71.020101
Shabani, A, and Lidar, D A. 2005.
"Completely positive post-Markovian master equation via a measurement approach". United States. https://doi.org/10.1103/PhysRevA.71.020101.
@article{osti_20650022,
title = {Completely positive post-Markovian master equation via a measurement approach},
author = {Shabani, A and Lidar, D A},
abstractNote = {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.},
doi = {10.1103/PhysRevA.71.020101},
url = {https://www.osti.gov/biblio/20650022},
journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 71,
place = {United States},
year = {Tue Feb 01 00:00:00 EST 2005},
month = {Tue Feb 01 00:00:00 EST 2005}
}
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