Kraus-Stinespring theorem

A Dynamical Map $\Lambda$ is Completely Positive iff $\forall \rho \exists \{L_{\alpha }{\}}_{\alpha }:\{\begin{array}{rl}{\sum }_{\alpha }{L}_{\alpha }^{†}{L}_{\alpha }& =1\\ {\sum }_{\alpha }{L}_{\alpha }^{†}\rho L_{\alpha }& =\Lambda [\rho ]\end{array}$