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A semi-quantum key distribution (SQKD) protocol allows two users, one of whom is
restricted in their quantum capabilities, to establish a shared secret key, secure against
an all-powerful adversary. In this paper, we design a new SQKD protocol using high-dimensional quantum states and conduct an information-theoretic security analysis.
We show that, similar to the fully-quantum key distribution case, high-dimensional
systems can increase the noise tolerance in the semi-quantum case. Along the way, we
prove several general security results which are applicable to other SQKD protocols
(both high-dimensional ones and standard qubit-based protocols).