Which differential equations correspond to the Lindblad equation?
Quantum Physics
2023-12-22 v2
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.
Keywords
Cite
@article{arxiv.2301.07887,
title = {Which differential equations correspond to the Lindblad equation?},
author = {Victor Kasatkin and Larry Gu and Daniel A. Lidar},
journal= {arXiv preprint arXiv:2301.07887},
year = {2023}
}
Comments
23 pages, 1 figure