Imperfect Measurement Devices Impact the Security of Tomography-Based Source-Independent Quantum Random Number Generator

Source-independent quantum random number generators (SI-QRNGs) can generate secure random numbers with untrusted and uncharacterized sources. Recently, a tomography-based SI-QRNG protocol has garnered significant attention for its higher randomness generation rate[Phys. Rev. A 99, 022328 (2019)], achieved through measurements utilizing three mutually unbiased bases. However, imperfect and inadequately characterized measurement devices would impact the security and performance of this protocol. In this work, considering the imperfect basis modulation, afterpulse effect and detection efficiency mismatch, it is demonstrated that the imperfect measurement devices would reduce the extractable randomness and lead to the incorrect estimation of the conditional min-entropy. Additionally, the influences of the finite-size effect and the performances of the protocol based on different parameter estimation methods are investigated and compared. To guarantee the security of generated random numbers, accurate conditional min-entropy estimation methods that are compatible with imperfect factors are also developed. The work emphasizes the significance of considering the imperfections in measurement devices and establishing tighter bounds for parameter estimation, especially in high-speed systems, thereby enhancing the robustness and performance of the protocol.