Controlled implementation of a nonlocal and open-target destination quantum controlled-Not （CNOT） gate using partially entangled pairs

We show how a nonlocal and open-target destination quantum controlled-Not （CNOT） gate can be probabilistically implemented by using partially entangled pairs of particles. We first investigate the controlled implementation of a nonlocal and three-target destination CNOT gate using three partially entangled pairs, and then generalize the scheme to the case of N -target destination. In this scheme, Alice’s local generalized measurement described by a positive operator valued measurement （POVM） plays a key role. We construct the required POVM. It is worth noting that deterministic and exact implementation of a nonlocal CNOT gate can be realized using partially entangled pairs.