Security proof for QKD systems with threshold detectors

TL;DR

This paper provides a rigorous security proof for BB84 and BBM92 quantum key distribution protocols with threshold detectors, confirming their robustness even when ideal qubit distillation isn't possible.

Contribution

It establishes that existing security proofs remain valid for practical detectors, extending the theoretical foundation of QKD security to real-world devices.

Findings

Security proofs hold with threshold detectors in BB84.

Higher error rates up to 20% are tolerable with two-way communication.

Security of BBM92 protocol with threshold detectors is also proven.

Abstract

In this paper, we rigorously prove the intuition that in security proofs for BB84 one may regard an incoming signal to Bob as a qubit state. From this result, it follows that all security proofs for BB84 based on a virtual qubit entanglement distillation protocol, which was originally proposed by Lo and Chau [H.-K. Lo and H. F. Chau, Science 283, 2050 (1999)], and Shor and Preskill [P. W. Shor and J. Preskill, Phys. Rev. Lett. 85, 441 (2000)], are all valid even if Bob's actual apparatus cannot distill a qubit state explicitly. As a consequence, especially, the well-known result that a higher bit error rate of 20% can be tolerated for BB84 protocol by using two-way classical communications is still valid even when Bob uses threshold detectors. Using the same technique, we also prove the security of the Bennett-Brassard-Mermin 1992 (BBM92) protocol where Alice and Bob both use threshold detectors.