Asymptotic Analysis of a Three State Quantum Cryptographic Protocol

In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-bound on the key rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key rate bound remains positive up to an error rate of $11\%$, exactly that achieved by the four-state BB84 protocol.