Kraus-Stinespring theorem

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