Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states

TL;DR

This paper explores the relationship between entanglement, Bell-inequality violation, and teleportation fidelity in two-qubit X states, showing that Bell-inequality violation guarantees usefulness for teleportation even with limited operations.

Contribution

It extends previous results by demonstrating that Bell-inequality violation in X states ensures nonclassical teleportation with restricted unitary operations.

Findings

Bell-inequality violation implies teleportation usefulness for X states.

Maximum fidelity difference with limited operations is 1/9.

Bell-inequality violation guarantees nonclassical teleportation in X states.

Abstract

Based on the assumption that the receiver Bob can apply any unitary transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)] proved that any mixed two spin-1/2 state which violates the Bell-CHSH inequality is useful for teleportation. Here, we further show that any X state which violates the Bell-CHSH inequality can also be used for nonclassical teleportation even if Bob can only perform the identity or the Pauli rotation operations. Moreover, we showed that the maximal difference between the two average fidelities achievable via Bob's arbitrary transformations and via the sole identity or the Pauli rotation is 1/9.