Security of a Semi-Quantum Protocol Where Reflections Contribute to the Secret Key

Abstract: In this paper we provide a proof of unconditional security for a semi-quantum key distribution protocol introduced in a previous work. This particular protocol demonstrated the possibility of using $X$ basis states to contribute to the raw key of the two users (as opposed to using only direct measurement results) even though a semi-quantum participant cannot directly manipulate such states. In this work we provide a complete proof of security by deriving a lower bound of the protocol's key rate in the asymptotic scenario. Using this bound we are able to find an error threshold value such that for all error rates less than this threshold, it is guaranteed that $A$ and $B$ may distill a secure secret key; for error rates larger than this threshold, $A$ and $B$ should abort. We demonstrate that this error threshold compares favorably to several fully quantum protocols. We also comment on some interesting observations about the behavior of this protocol under certain noise scenarios.