The Role of Localizable Concurrence in Quantum Teleportation Protocols

TL;DR

This paper demonstrates that localizable concurrence is a necessary quantum resource for multi-partite teleportation protocols to outperform classical methods, especially in noisy environments, extending previous results to general cases.

Contribution

It establishes that non-zero localizable concurrence is essential for quantum teleportation with multi-partite states, even when other entanglement measures vanish, broadening understanding of quantum resources.

Findings

Localizable concurrence is necessary for teleportation advantage.

Teleportation fidelity correlates with localizable concurrence under noise.

The result extends to arbitrary multi-partite teleportation protocols.

Abstract

Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multi-partite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multi-partite state, that includes a Bell measurement, requires a non-vanishing localizable concurrence between two of its parties in order to perform better than the classical protocol. By first analyzing the GHZ channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multi-partite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multi-partite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multi-partite entangled channel.