TY - JOUR

T1 - Finding the Kraus decomposition from a master equation and vice versa

AU - Andersson, Erika

AU - Cresser, James D.

AU - Hall, Michael J.W.

PY - 2007

Y1 - 2007

N2 - 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 N2N2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N2N2 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.

AB - 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 N2N2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N2N2 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.

UR - http://www.scopus.com/inward/record.url?scp=34548526935&partnerID=8YFLogxK

U2 - 10.1080/09500340701352581

DO - 10.1080/09500340701352581

M3 - Article

SN - 0950-0340

VL - 54

SP - 1695

EP - 1716

JO - Journal of Modern Optics

JF - Journal of Modern Optics

IS - 12

ER -