Complete positivity for time-dependent qubit master equations

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Title Complete positivity for time-dependent qubit master equations
Author Hall, Michael
Journal Name Journal of Physics A
Year Published 2008
Place of publication United Kingdom
Publisher Institute of Physics Publishing
Abstract It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is block-diagonal, then the necessary and sufficient conditions for completely positive evolution may be formulated in terms of the oscillator Hamiltonian or Lagrangian. When the solution of the oscillator equation is not known, an explicit sufficient condition for complete positivity can still be obtained, based on a Hamiltonian/Lagrangian inequality. A rotational form-invariance property is used to characterize the evolution via a single first-order nonlinear differential equation, enabling some further exact results to be obtained. A class of master equations is identified for which complete positivity reduces to the simpler condition of positivity.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1088/1751-8113/41/20/205302
Copyright Statement Copyright 2011 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.
Volume 41
Issue Number 20
Page from 205302-1
Page to 205302-14
ISSN 0305-4470
Date Accessioned 2011-12-05
Date Available 2012-03-06T05:48:13Z
Language en_US
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 Information, Computation and Communication
URI http://hdl.handle.net/10072/42437
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1x

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