Finding the Kraus decomposition from a master equation and vice versa
MetadataShow full item record
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.
Journal of Modern Optics
Copyright 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.
Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
Quantum Physics not elsewhere classified