Security analysis and improvement of source independent quantum random number generators with imperfect devices

Abstract

Recently, a source-independent quantum random number generator (SI-QRNG), which can generate secure random numbers with untrusted sources, has been realized. However, the measurement loopholes of the trusted but imperfect devices used in SI-QRNGs have not yet been fully explored. Here, we point out and evaluate the security loopholes of practical imperfect measurement devices in SI-QRNGs. We also provide corresponding countermeasures to prevent these information leakages by recalculating the conditional minimum entropy and adding a monitor. Furthermore, by taking into account the finite-size effect, we show that the influence of the afterpulse can exceed that of the finite-size effect with the large number of sampled rounds. Our protocol is simple and effective, and it promotes the security of SI-QRNG in practice as well as the compatibility with high-speed measurement evices, thus paving the way for constructing ultrafast and security-certified commercial SI-QRNG systems.