Secrecy in prepare-and-measure CHSH tests with a qubit bound

TL;DR

This paper proves that a key security bound in device-independent quantum key distribution, based on Bell inequality violations, also applies to prepare-and-measure protocols under a qubit assumption, bridging a gap between these approaches.

Contribution

It establishes that a known min entropy lower bound in DI QKD also holds for prepare-and-measure protocols with a qubit source, under minimal assumptions.

Findings

The min entropy bound applies in prepare-and-measure settings with a qubit source.

The result relies only on the source being limited to a two-dimensional Hilbert space.

This extends security proofs from entanglement-based to prepare-and-measure protocols.

Abstract

The security of device-independent (DI) quantum key distribution (QKD) protocols relies on the violation of Bell inequalities. As such, their security can be established based on minimal assumptions about the devices, but their implementation necessarily requires the distribution of entangled states. In a setting with fully trusted devices, any entanglement-based protocol is essentially equivalent to a corresponding prepare-and-measure protocol. This correspondence, however, is not generally valid in the DI setting unless one makes extra assumptions about the devices. Here we prove that a known tight lower bound on the min entropy in terms of the CHSH Bell correlator, which has featured in a number of entanglement-based DI QKD security proofs, also holds in a prepare-and-measure setting, subject only to the assumption that the source is limited to a two-dimensional Hilbert space.