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.
Mismatched measurements were used in @cite_2 in order to get better channel statistics for a single-state semi-quantum protocol first introduced in @cite_12 . Though single-state semi-quantum protocols utilize two-way quantum channels, they admit many simplifications which ease their security analysis. In this paper, we consider a multi-state semi-quantum protocol (which are more difficult to analyze) and show mismatched measurements improve its key-rate; indeed, our new key rate bound derived in this paper shows this semi-quantum protocol has the same noise tolerance as the fully-quantum BB84 protocol.
@cite_12 @cite_2
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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 @math , exactly that achieved by the four-state BB84 protocol. Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states @math and @math can contribute to key generation, and the third state @math is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used. We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure. Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter @math . Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.