Physics – Quantum Physics
Scientific paper
2008-01-27
J Mod. Opt. 54, 1695 (2007)
Physics
Quantum Physics
16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 2006
Scientific paper
10.1080/09500340701352581
For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed 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) diagonalising 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.
Andersson Erika
Cresser Jim D.
Hall Michael J. W.
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