Finding the Kraus decomposition from a master equation and vice versa

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Title Finding the Kraus decomposition from a master equation and vice versa
Author Andersson, Erika; Cresser, James D.; Hall, Michael
Journal Name Journal of Modern Optics
Year Published 2007
Place of publication United Kingdom
Publisher Taylor & Francis Ltd.
Abstract For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is given for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N 2×N 2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N 2×N 2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a “best possible” master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1080/09500340701352581
Copyright Statement Copyright 2007 Taylor & Francis. This is an electronic version of an article published in Journal of Modern Optics, Vol.54(12), 2007, pp.1695-1716. Journal of Modern Optics is available online at: http://www.tandfonline.com with the open URL of your article.
Volume 54
Issue Number 12
Page from 1695
Page to 1716
ISSN 0950-0340
Date Accessioned 2011-12-05; 2012-07-27T03:10:03Z
Date Available 2012-07-27T03:10:03Z
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory; Quantum Optics; Quantum Physics
URI http://hdl.handle.net/10072/46021
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1x

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