Michael Nielsen

Michael Nielsen proved a precise criterion for converting one pure quantum state of a bipartite quantum system into another using LOCC. If ${\lambda }_{\psi }$ and ${\lambda }_{\varphi }$ are the eigenvalue lists of their reduced density operators, the deterministic conversion $|\psi ⟩\to |\varphi ⟩$ is possible exactly when ${\lambda }_{\psi }\prec {\lambda }_{\varphi }$, a majorization condition. Thus the descending partial sums for the initial list must not exceed those for the target list. For example, $(1/2,1/2)\prec (1,0)$ permits converting a Bell state into a product state; the reverse conversion is forbidden by this criterion.^[ref]