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Markovian dynamics of open quantum systems are described by the L-GKSequation, known also as the Lindblad equation. The equation is expressed bymeans of left and right matrix multiplications. This formulation hampersnumerical implementations. Representing the dynamics by a matrix-vectornotation overcomes this problem. We review three approaches to obtain such arepresentation. The methods are demonstrated for a driven two-level systemsubject to spontaneous emission.

Three approaches for representing Lindblad dynamics by a matrix-vector notation