  We investigate a quantum repeater scheme for quantum key distribution based
on the work by Muralidharan et al., Phys. Rev. Lett. 112, 250501 (2014). Our
scheme extends that work by making use of error syndrome measurement outcomes
available at the repeater stations. We show how to calculate the secret key
rates for the case of optimizing the syndrome information, while the known key
rate is based on a scenario of coarse-graining the syndrome information. We
show that these key rates can surpass the Pirandola-Laurenza-Ottaviani-Banchi
bound on secret key rates of direct transmission over lossy bosonic channels.
