Featuring causal order in teleportation of two quantum teleportation channels

TL;DR

This paper investigates how controlling causal order in quantum teleportation channels can optimize fidelity, achieving perfect teleportation with optimal measurements even with noisy entangled resources.

Contribution

It analytically derives the fidelity for teleportation with arbitrary measurements on the control state and identifies conditions for perfect teleportation with noisy entanglement.

Findings

Optimal measurement on control state yields perfect teleportation.

Fidelity depends on the quality of the initial entangled resource.

Perfect teleportation is achievable despite noise with proper causal order control.

Abstract

Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource by using 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 measurement over such control state and then we get a perfect teleportation by selecting the optimal measurement on it. 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 probabilities of the control state but on the imperfect initial resource entangled.