Featuring Causal Order in Teleportation With Two Quantum Teleportation Channels

Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource being present in it by using additionally an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary initialization of such control state and performing an optimal measurement on it, thus obtaining a perfect teleportation. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the preparation of the control state but instead on the imperfect initial entangled resource.