Practical source-independent quantum random number generation with detector efficiency mismatch

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.