Multi-Mediated Semi-Quantum Key Distribution

A semi-quantum key distribution (SQKD) protocol allows two users $A$ and $B$ to establish a shared secret key that is secure against an all-powerful adversary $E$ even when one of the users (e.g., $B$) is semi-quantum or classical in nature while the other is fully-quantum. A mediated SQKD protocol allows two semi-quantum users to establish a key with the help of an adversarial quantum server. We introduce the concept of a multi-mediated SQKD protocol where two (or more) adversarial quantum servers are used. We construct a new protocol in this model and show how it can withstand high levels of quantum noise, though at a cost to efficiency. We perform an information theoretic security analysis and, along the way, prove a general security result applicable to arbitrary MM-SQKD protocols. Finally, a comparison is made to previous (S)QKD protocols.