Abstract: Parameter estimation(the yield and the phase error rate of the single photon) is a major factor that affects the key rate of decoy state MDI-QKD. This paper investigates the issues of parameter estimation in MDI-QKD with a spontaneous parametric down conversion (SPDC) source with a joint estimation method. Different from the existing separate estimation method, we derive analytical solutions to the parameters from the equation set of the average count rate and error rate, and then analyze it as a unitary function conceding the relevance between the two parameters. Through looking at the minimum of the function in the closed interval, a tighter estimation of the secure key rate is obtained. This method provides a new way to increase the performance of the MDI-QKD protocol.

Key words: Quantum Key Distribution, decoy state, Measurement Device-Independent, Spontaneous Parametric Down Conversion Source, statistical fluctuation

摘要： 参数估计（单光子计数率与误码率）是影响诱骗态MDI-QKD（Measurement Device-Independent Quantum key distribution）成码率的重要因素。本文采用综合估计的方法，研究采用自发参量下转换（spontaneous parametric down conversion，SPDC）源的MDI-QKD参数估计问题。不同于已有的独立估计方法，本文从平均计数率和误码率方程组中得到参数解析式，然后充分考虑参数之间的关联性，将其作为一个整体函数进行分析。通过在闭区间内求函数最小值，给出了更紧的安全码率估计。该方法为进一步提升此类MDI-QKD协议的性能提供了思路。

关键词: 量子密钥分配, 诱骗态, 测量设备无关, 自发参量下转换源, 统计涨落