Average Fidelity of Two Qubits Entanglement Teleportation Mediated Via a Single Majorana Wire

We revisit the teleportation of two qubits entanglement using a single channel made of a single Majorana wire connecting two pairs of qubits each at the sending and receiving ends of the wire. The scheme is different from that use in our early work (Phys. Scr. 95 035803 (2020)) where the two qubit teleportation required two copies of the Majorana wires setup as required to implement the Lee and Kim teleportation scheme. The two pairs of qubit interact via the exchange coupling. It is in this setting that we investigate the role of the exchange coupling, the channel parameters, the spin chain parameters on the average fidelity of entanglement teleportation. We equally consider the fact that the geographically located two pairs of qubits interact differently with their respective spin chain environment. The dynamics of the average fidelity is shown to be enhanced when using a set-up with symmetric coupling between qubits and Majorana wire at both ends as compared to when using asymmetric coupling. Small values of the coupling between the qubits and spin environments should however be used. Large values of the exchange coupling between qubits in the two sub-systems should be used to have high fidelity of the teleported state. The dynamics of the average fidelity of entanglement teleportation is seen to depend on the size of the spin environment as compared to the teleportation protocol used in our earlier work where the dynamics is mildly sensitive to the size of the spin environment. Increasing the strength of the transverse magnetic field and large values of the anisotropy degree enhances the average fidelity of entanglement teleportation. The same observation is seen when considering the same values of the coupling between the two qubits sub-systems at the opposite ends of the Majorana wire and their respective spin environment. The dynamics of the system is however seen to observe almost a similar trend as that of the above cited work for the single Majorana wire setup.