Finite-key analysis of the six-state protocol with photon-number-resolution detectors

TL;DR

This paper derives a finite-key lower bound for the six-state quantum key distribution protocol using photon-number-resolving detectors, highlighting the importance of finite-size effects in practical implementations.

Contribution

It provides a novel finite-key analysis for the six-state protocol with untrusted sources and photon-number-resolving detectors, including explicit formulas for practical scenarios.

Findings

Finite-key corrections are significant and must be considered in real implementations.

The key rate depends on channel losses and source characteristics.

Finite resources impact the achievable secure key rate.

Abstract

The six-state protocol is a discrete-variable protocol for quantum key distribution, that permits to tolerate a noisier channel than the BB84 protocol. In this work we provide a lower bound on the maximum achievable key rate of a practical implementation of the entanglement-based version of the six-state protocol. Regarding the experimental set-up we consider that the source is untrusted and the photon-number statistics is measured using photon-number-resolving detectors. We provide the formula for the key rate for a finite initial number of resources. As an illustration of the considered formalism, we calculate the key rate for the setting where the source produces entangled photon pairs via parametric down-conversion and the losses in the channel depend on the distance. As a result we find that the finite-key corrections for the considered scenario are not negligible and they should be considered in any practical analysis.