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A quantum random-number generator (QRNG) can theoretically generateunpredictable random numbers with perfect devices and is an ideal and securesource of random numbers for cryptography. However, the practicalimplementations always contain imperfections, which will greatly influence therandomness of the final output and even open loopholes to eavesdroppers.Recently, Thewes et al. experimentally demonstrated a continuous-variableeavesdropping attack, based on heterodyne detection, on a trustedcontinuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in manyother practical continuous-variable QRNG studies, they always supposed thelocal oscillator was stable and ignored its fluctuation which might lead tosecurity threats such as wavelength attack. In this work, based on the theoryof the conditional min-entropy, imperfections of the practical security ofcontinuous-variable QRNGs are systematically analyzed, especially the localoscillator fluctuation under imbalanced homodyne detection. Experiments of apractical QRNG based on vacuum fluctuation are demonstrated to show theinfluence of local oscillator fluctuation on the total measurement noisevariances and the practical conditional min-entropy with beam splitters ofdifferent transmittances. Moreover, a local oscillator monitoring method isproposed for the practical continuous-variable QRNG, which can be used tocalibrate the practical conditional min-entropy.

Practical security analysis of a continuous-variable quantum random number generator with a noisy local oscillator