Finding the Kraus decomposition from a master equation and vice versa

Erika Andersson, James D. Cresser, Michael J. W. Hall

Research output: Contribution to journalArticle

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 x N-2 matrix time evolution ( to obtain the completely positive map), and ( ii) diagonalizing a related N-2 x 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.

Original languageEnglish
Pages (from-to)1695-1716
Number of pages22
JournalJournal of Modern Optics
Volume54
Issue number12
DOIs
Publication statusPublished - 2007

Cite this

Andersson, Erika ; Cresser, James D. ; Hall, Michael J. W. / Finding the Kraus decomposition from a master equation and vice versa. In: Journal of Modern Optics. 2007 ; Vol. 54, No. 12. pp. 1695-1716.
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Finding the Kraus decomposition from a master equation and vice versa. / Andersson, Erika; Cresser, James D.; Hall, Michael J. W.

In: Journal of Modern Optics, Vol. 54, No. 12, 2007, p. 1695-1716.

Research output: Contribution to journalArticle

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