Purification and correlated measurements of bipartite mixed states
Jan Bouda, Vladimír Bužek · Physical Review A · 2002
We prove that all purifications of a nonfactorable state (i.e., the state that cannot be expressed in a form ${\ensuremath{\rho}}_{\mathrm{AB}}={\ensuremath{\rho}}_{A}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{B})$ are entangled. We also show that for any bipartite state there exists a pair of measurements that are correlated on this state if and only if the state is nonfactorable.