Entanglement Swapping for Cluster-Class States and Its Applications in Quantum Information Processing

Entanglement swapping for four-qubit cluster-class states is studied. It is shown that a four-qubit cluster state (maximally entangled) can be obtained with a certain probability from two four-qubit cluster-class states by entanglement swapping. The probability is related to the smallest superposition coefficient of the cluster-class states (when all the moduli of amplitudes are equivalent, they are the usual cluster states and the probability hits to one). Two examples for the applications of the entanglement swapping are also presented. One is quantum teleportation of an arbitrary two-qubit state via a quantum repeater, in which the success probability can be improved by the entanglement swapping when the quantum channels are general cluster-class states (partially entangled). The other is quantum key distribution, in which a secret random sequence of bits (a “key”) can be efficiently established between two distant parties by the entanglement swapping of two groups of cluster states.