| Quantum cryptology is a combination of quantum mechanics and cryptology. Quantum key distribution(QKD), as the core of quantum cryptology, admits two remote parties to share an unconditional security key, which is guaranteed by the quantum mechanics and has been proved in theory. However, the setups used in the practical system are imperfect,which will leave some loopholes for Eve to spy the secret key.This thesis mainly focuses on the theoretical study of measurement-device-independent quantum key distribution with a passive decoy-state method. Our goal is to provide a good theory evidence for experiment. The main two parts are shown as follows.Firstly, we consider the models of measurement-device-independent quantum key distribution(MDI-QKD), decoy state method, and passive decoy-state method. MDIQKD can remove all the detector loopholes. When it is combined with decoy-state method,the final key is unconditionally secure, even if Alice and Bob do not have strict singlephoton sources. However, active modulation of source intensity, which is used to generate the decoy state, may leave side channels and leak additional information to Eve, which can be solved by passive decoy-state method. In passive decoy-state method, Alice or Bob passively chooses a signal state or a decoy state according to the responding of a detector in the source part.Secondly, we consider the MDI-QKD with a passive decoy-state method, in which both Alice and Bob send pulses to an untrusted third party, Charlie. Then, in order to estimate the key generation rate, we derive two tight formulas to estimate the lower bound of yield and the upper bound of error rate that both Alice and Bob send single photon pulse to Charlie. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account, based on the standard statistical analysis. |
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