In this paper, we derive key-rate expressions for different quantum key distribution protocols. Our key-rate equations utilize multiple channel statistics, including those gathered from mismatched measurement bases - i.e., when Alice and Bob choose incompatible bases. In particular, we will consider an Extended B92 and a two-way semi-quantum protocol. For both these protocols, we demonstrate that their tolerance to noise is higher than previously thought - in fact, we will show the semi-quantum protocol can actually tolerate the same noise level as the fully quantum BB84 protocol. Along the way, we will also consider an optimal QKD protocol for various quantum channels. Finally, all the key-rate expressions which we derive in this paper are applicable to any arbitrary, not necessarily symmetric, quantum channel.
Abstract We show that rejected-data protocols for quantum cryptography are secure against generalized intercept resend strategies of an eavesdropper provided that the legitimate users of the communication channel use at least three bases. We discuss the connection between this result and the recently-developed protocol based on violations of a suitably-constructed Bell-type inequality for single particles. We also give a new estimate of the probability that an eavesdropper remains undetected under the original protocol and thereby show that the optimal strategies available to an eavesdropper are further limited to those which randomize the errors between the sub-ensembles of data. This result also has implications for the way in which the legitimate users of the channel choose their test data.