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arXiv · 2301.07887

Which differential equations correspond to the Lindblad equation?

Victor Kasatkin·Larry Gu·Daniel A. Lidar
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Abstract

The Lindblad master equation can always be transformed into a first-order linear ordinary differential equation (1ODE) for the coherence vector. We pose the inverse problem: given a finite-dimensional, non-homogeneous 1ODE, does a corresponding Lindblad equation exist? If so, what are the corresponding Hamiltonian and Lindblad operators? We provide a general solution to this problem, including a complete positivity test in terms of the parameters of the 1ODE. We also derive a host of properties relating the two representations (master equation and 1ODE), which are of independent interest.

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Victor Kasatkin, Larry Gu, Daniel A. Lidar. 2023-01-19. Which differential equations correspond to the Lindblad equation?. https://doi.org/10.1103/physrevresearch.5.043163

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