Finding the Kraus decomposition from a master equation and vice versa | Macquarie University ResearchOnline

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Title: Finding the Kraus decomposition from a master equation and vice versa
Related: Journal of modern optics, Vol. 54, Issue 12, p.1695-1716
DOI: 10.1080/09500340701352581
Publisher: Taylor and Francis Ltd
Date: 2007
Author/Creator: Andersson, Erika
Author/Creator: Cresser, James D
Author/Creator: Hall, Michael J. W
Description: 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 N²xN² matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N²xN² 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.
Description: 22 page(s)
Resource Type: journal article
Organisation: Macquarie University. Dept. of Physics

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