Finding the Kraus decomposition from a master equation and vice versa
| dc.creator | Andersson, Erika | |
| dc.creator | Cresser, Jim D. | |
| dc.creator | Hall, Michael J. W. | |
| dc.date | 2008-01-27 | |
| dc.date.accessioned | 2026-07-07T08:56:43Z | |
| dc.date.available | 2026-07-07T08:56:43Z | |
| dc.description | 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. | |
| dc.description | 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 2006 | |
| dc.identifier | https://arxiv.org/abs/0801.4100 | |
| dc.identifier | http://arxiv.org/abs/0801.4100 | |
| dc.identifier | J Mod. Opt. 54, 1695 (2007) | |
| dc.identifier | doi:10.1080/09500340701352581 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146711 | |
| dc.subject | Quantum Physics | |
| dc.title | Finding the Kraus decomposition from a master equation and vice versa | |
| dc.type | text |