  In this paper we present a new proof technique for semi-quantum key
distribution protocols which makes use of a quantum entropic uncertainty
relation to bound an adversary's information. Our new technique provides a more
optimistic key-rate bound than previous work relying only on noise statistics
(as opposed to using additional mismatched measurements which increase the
noise tolerance of this protocol, but at the cost of requiring four times the
amount of measurement data). Our new technique may hold application in the
proof of security of other semi-quantum protocols or protocols relying on
two-way quantum communication.
