  This article provides the unconditional security of a semi quantum key
distribution (SQKD) protocol based on 3-dimensional quantum states. By deriving
a lower bound for the key rate, in the asymptotic scenario, as a function of
the quantum channel's noise, we find that this protocol has improved secret key
rate with much more tolerance for noise compared to the previous 2-dimensional
SQKD protocol. Our results highlight that, similar to the fully quantum key
distribution protocol, increasing the dimension of the system can increase the
noise tolerance in the semi-quantum key distribution, as well.
