Quantum Tasks with Non-maximally Quantum Channels via Positive Operator-Valued Measurement

By using a proper positive operator-valued measure (POVM), we present two new schemes for probabilistic transmission with non-maximally four-particle cluster states. In the first scheme, we demonstrate that two non-maximally four-particle cluster states can be used to realize probabilistically sharing an unknown three-particle GHZ-type state within either distant agent’s place. In the second protocol, we demonstrate that a non-maximally four-particle cluster state can be used to teleport an arbitrary unknown multi-particle state in a probabilistic manner with appropriate unitary operations and POVM. Moreover the total success probability of these two schemes are also worked out.