  Quantum key distribution (QKD) allows two parties to establish a shared
secret key that is secure against all-powerful adversaries. One such protocol
named B92 is quite appealing due to its simplicity but is highly sensitive to
channel noise. In this work, we investigate a high-dimensional variant of an
extended version of the B92 protocol and show that it can distill a key over
high noise channels. The protocol we consider requires that Alice send only
three high-dimensional states and Bob only perform partial measurements. We
perform an information-theoretic security analysis of our protocol and compare
its key rate to that of a high-dimensional BB84 protocol over depolarization
and amplitude damping channels.
