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Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda i(\rho_{10}-\rho_{01})+\lambda^2\rho_{11} & \lambda i(\rho_{11} -\rho_{00})+\lambda^2 \rho_{01} \\ \lambda i(\rho_{00}-\rho_{11}) +\la...