Tripartite Probabilistic and Controlled Teleportation of an Arbitrary Single-Qubit State via One-Dimensional Four-Qubit Cluster-Type State

A tripartite scheme for probabilistically teleporting an arbitrary single-qubit state with one-dimensional four-qubit cluster-type state as the quantum channel is proposed. In the scheme, both of the sender and the controller perform a Bell-state measurement (BSM) on their respective qubit pair and announce the measurement results via classical communication. With the help of the sender and the controller, the receiver can reconstruct the original state with a certain probability by introducing an auxiliary qubit and making appropriate unitary operations and measurement. In addition, the total success probability and classical message cost of the present scheme are also worked out.