Relating EPR steering with the fidelity of quantum teleportation for two- and three-qubit states

Einstein–Podolsky–Rosen (EPR) steering is an important quantum resource in quantum information and computation. The relationships between EPR steering and the fidelity of quantum teleportation for two- and three-qubit states are investigated in this paper. For two-qubit states, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the two-qubit X-type states which violate the three-setting measurements steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of two-qubit reduced states for three-qubit pure states maintain the same ordering. The complementary relations between the steering observables and the average teleportation fidelities for three-qubit pure states are also established.