Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This work analyzes evolutions in the extractable amount of randomness with increasing the Hilbert space dimension, state preparation subspace, or measurement subspace in a class of semi-device-independent quantum-RNG, where bounding the states’ overlap is the core assumption, built on the prepare-and-measure scheme. We further discuss the effect of these factors on the complexity and draw a conclusion on the optimal scenario. We investigate the generic case of time-bin encoding scheme, define various input (state preparation) and outcome (measurement) subspaces, and discuss the optimal scenarios to obtain maximum entropy. Several input designs were experimentally tested and analyzed for their conceivable outcome arrangements. We evaluated their performance by considering the device’s imperfections, particularly the after-pulsing effect and dark counts of the detectors. Finally, we demonstrate that this approach can boost the system entropy, resulting in more extractable randomness.

中文翻译：

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具有未表征设备的广义时间仓量子随机数生成器

与伪随机数生成器和硬件随机数生成器等传统生成器相比，基于量子力学的随机数生成器（RNG）因其安全性和不可预测性而备受关注。这项工作分析了一类半设备无关的量子 RNG 中随着希尔伯特空间维度、状态准备子空间或测量子空间的增加，可提取的随机性量的演变，其中限制状态重叠是核心假设，建立在准备和测量方案。我们进一步讨论这些因素对复杂性的影响，并得出最佳方案的结论。我们研究时间仓编码方案的一般情况，定义各种输入（状态准备）和结果（测量）子空间，并讨论获得最大熵的最佳场景。对几种输入设计进行了实验测试并分析了其可想象的结果安排。我们通过考虑设备的缺陷，特别是探测器的后脉冲效应和暗计数来评估它们的性能。最后，我们证明这种方法可以提高系统熵，从而产生更多可提取的随机性。