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  • Finding the Kraus decomposition from a master equation and vice versa

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    Author(s)
    Andersson, Erika
    Cresser, James D
    Hall, Michael JW
    Griffith University Author(s)
    Hall, Michael J.
    Year published
    2007
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    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׎ 2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N 2׎ 2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and ...
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    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׎ 2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N 2׎ 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.
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    Journal Title
    Journal of Modern Optics
    Volume
    54
    Issue
    12
    DOI
    https://doi.org/10.1080/09500340701352581
    Copyright Statement
    © 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.
    Subject
    Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
    Atomic, molecular and optical physics
    Quantum physics
    Quantum optics and quantum optomechanics
    Quantum physics not elsewhere classified
    Nanotechnology
    Publication URI
    http://hdl.handle.net/10072/46021
    Collection
    • Journal articles

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