We present a quantum random number generator (QRNG) based on the random outcomes inherent in projective measurements on a superposition of quantum states of light. First, we use multiplexed holograms encoded on a spatial light modulator to spatially map down-converted photons onto a superposition of optical paths. This gives us full digital control of the mapping process which we can tailor to achieve any desired probability distribution. More importantly, we use this method to account for any bias present within our transmission and detection system, forgoing the need for time-consuming and inefficient unbiasing algorithms. Our QRNG achieved a min-entropy of $H_{\text{min}}=0.9991\pm 0.0003$ bits per photon and passed the NIST Statistical Test Suite. Furthermore, we extend our approach to realize a QRNG based on photons entangled in their orbital angular momentum (OAM) degree of freedom. This combination of digital holograms and projective measurements on arbitrary OAM combinations allowed us to generate random numbers with arbitrary distributions, in effect tailoring the system's entropy while maintaining the inherent quantum irreproducibility. Such techniques allow access to the higher-dimensional OAM Hilbert space, opening up an avenue for generating multiple random bits per photon.

中文翻译：

---

纠缠纠缠光子的全息控制随机数

我们基于在光的量子态叠加上的投影测量中固有的随机结果，提出了一个量子随机数发生器（QRNG）。首先，我们使用在空间光调制器上编码的多路全息图，将降频转换后的光子空间映射到光路的叠加上。这为我们提供了映射过程的完全数字控制，我们可以对其进行调整以实现任何所需的概率分布。更重要的是，我们使用这种方法来解决传输和检测系统中存在的任何偏差，从而无需耗时且效率低下的无偏差算法。我们的QRNG的最小熵为$H_{\text{分}}=0.9991\pm 0.0003$每光子位数，并通过了NIST统计测试套件。此外，我们扩展了方法，以基于纠缠在其轨道角动量（OAM）自由度中的光子实现QRNG。数字全息图和对任意OAM组合的投影测量的这种组合使我们能够生成具有任意分布的随机数，从而有效地调整了系统的熵，同时保持了固有的量子不可再现性。这样的技术允许访问更高维的OAM希尔伯特空间，从而为每个光子生成多个随机位开辟了一条途径。