Violation of Clauser–Horne–Shimony–Holt inequality and teleportation enhanced for a class of two-qubit X-states resulting from entanglement swapping

We consider entanglement swapping with two copies of a class of two-qubit X-states which do not violate Clauser---Horne---Shimony---Holt (CHSH) inequality or exceed the maximal classical teleportation fidelity. It is shown that there exists a class of initial states for which that the final states violate CHSH inequality or exceed the maximal classical channel for some results of Bell measurements. This implies that, by using entanglement swapping, it is possible to increase the violation of CHSH inequality or teleportation fidelity probabilistically. We also demonstrate that the activation of violating CHSH inequality does not represent the increase in entanglement.