Remote state preparation using positive operator-valued measures

► We find an one-to-one correspondence between local operators with respect to pure state with maximal Schmidt number. ► A compact form of the reduced state on Bobʼs system after Aliceʼs local pure operation is found. ► Relationships between Bobʼs states after two Aliceʼs local pure operations related by a unitary transformation is found. ► A construction of a POVM for any state including mixed states to prepare remotely is provided.