Despite the availability of commercial QRNG devices, distinguishing between PRNG and QRNG outputs computationally remains challenging. This paper 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 (security), efficiency (randomness and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances security but increases cost and decreases the generation rate. A shorter external reference cycle boosts security but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances security 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：尽管商用QRNG设备已普及，但通过计算区分PRNG与QRNG输出仍具挑战性。本文从QRNG制造商和用户的双重视角提出两项重要贡献。对制造商而言，传统基于单光子QRNG的量子性评估方法——通过光子计数的均值与方差比较——因有限样本量而在统计上不可靠。鉴于单光子的亚泊松统计特性，确认底层分布对于验证QRNG的量子性至关重要。我们提出一种更高效的双重统计方法，可在指定置信水平下确保光源的量子性。此外，我们证明在设备噪声影响下，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量及$\epsilon$-随机性条件。从用户视角看，QRNG的核心参数包括量子性（安全性）、效率（随机性与随机数生成速率）以及成本。我们的分析表明，这些参数取决于三个因素：单位时间预期光子数、外部参考周期时长和探测效率。较低的预期光子数可提升安全性，但会增加成本并降低生成速率；较短的外部参考周期能增强安全性，但需超过最小阈值以最小化时序误差，且对成本与速率影响较小；较低的探测效率可提高安全性并降低成本，但会减缓生成速率。最后，为验证结论，我们使用上述参数的不同取值进行数据模拟，并执行NIST、Dieharder、AIS-31、ENT等统计测试。本研究有助于制造商定制化开发更贴合用户需求的QRNG设备。