Entanglement is not sufficient for most practical entanglement-based QKD protocols

TL;DR

This paper demonstrates that entanglement alone does not guarantee the usefulness of states for practical entanglement-based QKD protocols, especially under realistic conditions with classical leakage, impacting the scalability of quantum networks.

Contribution

It identifies classes of entangled states that cannot be used for key extraction in practical protocols, even with minimal classical leakage, and provides bounds on QKD network scalability.

Findings

Certain entangled states are useless for key extraction under practical conditions.

Classical leakage significantly reduces the effectiveness of entanglement-based QKD.

Scalability of QKD networks is limited by noise and state properties.

Abstract

Quantum key distribution (QKD) is the most explored application of quantum information theory. A central problem in entanglement-based QKD (EB-QKD), is whether every entangled state can be used to extract a key. We observe that entanglement is not sufficient for standard practical EB-QKD protocols where the input choices are announced by the parties that want to share a secure key, such as E91 or entanglement-based BB84 type protocols, when even an arbitrarily small amount of leakage of classical side information occurs. We do this by identifying a class of two-qubit isotropic states that are entangled but cannot be used to distil the key under such protocols for any possible measurement by the parties. Counter-intuitively, this gap persists even when the leakage occurs from the "junk" rounds of the protocol, i.e, rounds that cannot be used to generate any key. We then extend this result to arbitrary dimensions and parties by identifying a class of isotropic states that are not useful to extract a secure key under such protocols, even if they are entangled. Finally, we demonstrate that our approach provides a tool to upper-bound the scalability of repeater-based QKD architectures in a protocol-independent manner. Interestingly, we find that allowing for even a tiny noise in the preparation drastically reduces the scalability of the QKD network.