Activation of entanglement in teleportation

TL;DR

This paper analyzes how entanglement activation in teleportation depends on classical communication and system dimension, deriving average fidelity with noisy channels and identifying thresholds for quantum advantage.

Contribution

It provides a derivation of teleportation fidelity with noisy classical channels without assuming shared entangled states, revealing classical communication thresholds for quantum advantage.

Findings

Entanglement activation requires a threshold amount of classical communication.

The classical communication needed depends on system dimension d.

Maximum classical communication needed occurs at d=4.

Abstract

We study the activation of entanglement in teleportation protocols. To this end, we a present derivation of the average fidelity of teleportation process with noisy classical channel for qudits. In our work we do not make any assumptions about the entangled states shared by communicating parties. Our result allows us to specify the minimum amount of classical information required to beat the classical limit when the protocol is based on the Bell measurements. We also compare average fidelity of teleportation obtained using noisy and perfect classical channel with restricted capacity. The most important insight into the intricacies of quantum information theory that we gain is that though entanglement, obviously, is a necessary resource for efficient teleportation it requires a certain threshold amount of classical communication to be more useful than classical communication. Another interesting finding is that the amount of classical communication required to activate entanglement for teleportation purposes depends on the dimension d of the system being teleported but is not monotonic reaching maximum for d = 4.