Semi device independence of the BB84 protocol

TL;DR

This paper establishes a semi device-independent security proof for the BB84 quantum key distribution protocol, assuming only one user's device is limited to a qubit Hilbert space, and derives an explicit key rate bound.

Contribution

It provides the first analytic lower bound on the secret key rate for semi device-independent BB84 under collective attacks with only one trusted qubit device.

Findings

Derived an explicit lower bound on the asymptotic secret key rate.

The result applies to noisy correlations and reduces to Shor-Preskill rate in ideal cases.

Proves security assuming only one device is a qubit, enhancing practical trust assumptions.

Abstract

The BB84 quantum key distribution protocol is semi device independent in the sense that it can be shown to be secure if just one of the users' devices is restricted to a qubit Hilbert space. Here, we derive an analytic lower bound on the asymptotic secret key rate for the entanglement-based version of BB84 assuming only that one of the users performs unknown qubit POVMs. The result holds against the class of collective attacks and reduces to the well known Shor-Preskill key rate for correlations corresponding to the ideal BB84 correlations mixed with any amount of random noise.