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.
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