Extraction of pure entangled states from many-body systems by distant local projections

We study the feasibility of extracting a pure entangled state of noncomplementary and potentially well-separated regions of a quantum many-body system. It is shown that this can indeed be accomplished in nonequilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as the magnetization of separated blocks of spins. A general procedure which can search for the optimal way to extract a pure entangled state through local projections is presented. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.