Teleportation is necessary for faithful quantum state transfer through noisy channels of maximal rank

TL;DR

This paper proves that quantum teleportation is both necessary and sufficient for faithful quantum state transfer through noisy channels of maximal rank with a single use, establishing its fundamental role in quantum communication.

Contribution

It demonstrates that quantum teleportation resources are essential and cannot be replaced by alternative protocols for certain noisy quantum channels.

Findings

Teleportation is necessary for faithful state transfer in maximal rank channels.

Quantum teleportation is sufficient for deterministic, faithful transfer.

No alternative protocols can replace teleportation for these channels.

Abstract

Quantum teleportation enables deterministic and faithful transmission of quantum states, provided a maximally entangled state is pre-shared between sender and receiver, and a one-way classical channel is available. Here, we prove that these resources are not only sufficient, but also necessary, for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the cannel is admitted. In other words, for this family of channels, there are no other protocols, based on different (and possibly cheaper) sets of resources, capable of replacing quantum teleportation.