This work presents two significant contributions from the perspectives of QRNG manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG's quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibit similarity under device noise, deriving corresponding photon statistics and conditions for $\epsilon$-randomness. From the user's perspective, the fundamental parameters of a QRNG are quantumness, efficiency (random entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc. over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.

翻译：本研究从量子随机数生成器（QRNG）制造商与用户的双重视角提出了两项重要贡献。对于制造商而言，传统上通过比较光子计数的均值与方差来评估基于单光子的QRNG的量子性，由于样本量有限，该方法在统计上并不可靠。鉴于单光子的亚泊松统计特性，确认其底层分布对于验证QRNG的量子性至关重要。我们提出了一种更高效的双重统计方法，以确保光学源在所需置信水平下具有量子性。此外，我们证明了在设备噪声下，服从指数分布与均匀分布的QRNG输出具有相似性，并推导了相应的光子统计特性以及实现$\epsilon$-随机性所需的条件。从用户视角来看，QRNG的基本参数包括量子性、效率（随机熵与随机数生成速率）以及成本。我们的分析表明，这些参数取决于三个因素：单位时间内的期望光子数、外部参考周期时长以及探测效率。较低的期望光子数可提升熵值，但会增加成本并降低生成速率；较短的外部参考周期能提高熵值，但必须超过最小阈值以最小化定时误差，且对成本与速率影响较小；较低的探测效率可增强熵值并降低成本，但会降低生成速率。最后，为验证我们的结果，我们使用上述参数的不同取值进行数据模拟，并执行了NIST、Dieharder、AIS-31、ENT等统计测试。本研究结论有助于制造商根据用户需求有效定制QRNG。