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Title: 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:
 [1];  [2]
  1. Physics Department and Center for Quantum Information and Quantum Control, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7 (Canada)
  2. 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}
}