A quantum cloning bound and application to quantum key distribution

TL;DR

This paper presents a new quantum cloning bound that enhances security proofs for the BB84 quantum key distribution protocol, especially under practical imperfections and arbitrary source states, leading to improved keyrate bounds.

Contribution

Introduces a quantum cloning bound applicable to prepare-and-measure QKD, enabling simpler security proofs and better keyrate bounds under realistic conditions.

Findings

Derives a keyrate bound for BB84 with arbitrary pure states.

Provides improved keyrate results over previous entropic uncertainty methods.

Offers stronger bounds when the source emits arbitrary qubit states and detectors are two-dimensional.

Abstract

We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proof of the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol against collective attacks. The approach we propose is able to handle the practical problem of source and detector alignment imprecisions in a simple way. Specifically, we derive a keyrate bound for a BB84 implementation in which Alice's source emits four given but arbitrary pure states, where the usual equivalence between prepare-and-measure and entanglement-based QKD no longer applies. Our result is similar to a keyrate derived by Mar{\o}y et. al. [Phys. Rev. A 82, 032337 (2010)] and generally an improvement over the keyrate derivable from the entropic uncertainty relation in situations where it applies. We also provide a stronger result for a source emitting arbitrary qubit states, and a further improved result if the detector is additionally assumed two dimensional.