Quantum random number generators (QRNGs) are widely used in information processing tasks. The quality of the random numbers obtained from QRNGs relies on the accurate characterization of the physical implementations. In practice, realistic devices are difficult to characterize, resulting in incorrect entropy estimations of the output random numbers. Recently, a novel quantum random number generation (QRNG) scheme, referred to as source-independent QRNG (SIQRNG), has attracted a lot of interest. The scheme can provide certified randomness by using untrusted and uncharacterized sources, under the assumption that the measurement devices are trusted. However, realistic devices inevitably feature imperfections. Here, we show that the output randomness of SIQRNG is compromised in the presence of detection imperfection , by constructing an attack based on a time-domain detection efficiency mismatch between two practical detectors. More importantly, we provide an unconditional security proof of SIQRNG that takes detection efficiency mismatch into account. In addition, we provide a parameter optimization method to effectively improve the final random number generation rate. Our work demonstrates that SIQRNG is highly practical and that randomness can be extracted even in the presence of a detection efficiency mismatch.

量子随机数发生器（QRNG）广泛用于信息处理任务。从QRNG获得的随机数的质量取决于物理实现的准确表征。实际上，现实的设备难以表征，从而导致输出随机数的熵估计不正确。最近，一种新颖的量子随机数生成（QRNG）方案，称为与源无关的QRNG（SIQRNG），引起了很多兴趣。在测量设备是可信的假设下，该方案可以通过使用不受信任和未经表征的来源来提供经证明的随机性。然而，现实的设备不可避免地具有缺陷。在这里，我们表明在存在检测缺陷的情况下，SIQRNG的输出随机性受到损害，通过基于两个实际检测器之间的时域检测效率不匹配构造攻击。更重要的是，我们提供了SIQRNG的无条件安全证明，其中考虑了检测效率不匹配的问题。此外，我们提供了一种参数优化方法，可有效提高最终随机数的生成率。我们的工作表明，SIQRNG非常实用，即使在检测效率不匹配的情况下也可以提取随机性。