Entanglement splitting of pure bipartite quantum states

The concept of entanglement splitting is introduced by asking whether it is possible for a party possessing half of a pure bipartite quantum state to transfer some of his entanglement with the other party to a third party. We describe the unitary local transformation for symmetric and isotropic splitting of a singlet into two branches that leads to the highest entanglement of the output. The capacity of the resulting quantum channels is discussed. Using the same transformation for less than maximally entangled pure states, the entanglement of the resulting states is found. We discuss whether they can be used to do teleportation and to test the Bell inequality. Finally, we generalize to entanglement splitting into more than two branches.