# Characterization of a Quantum Random Number Generator Based on Vacuum Fluctuations
## 1 Introduction  
Reliable random numbers (RNs) fulfil an essential role in multiple applications, such as gambling, computer simulations, statistical analysis, or cryptography [1, 2]. Traditionally, pseudo-random number generators (PRNGs) have been able to suppress this demand through fast, and easily implemented deterministic algorithms. Unfortunately, their output is only dependent on an initial seed and the algorithm itself, and, therefore, becomes predictable to an adversary with enough computational resources, as an inherent periodicity can be found [2, 3]. As a result, their implementation is not suitable for critical applications, such as quantum key distribution (QKD), where true unpredictability is required [4, 5]. In answer to these shortcomings, hardware-based implementations have been developed. These extract randomness from measurements of some apparently unpredictable physical process, such as atmospheric or electrical noise [6, 7]. However, such devices are generally slow and difficult to implement as the yielded entropy is hard to quantify due to their susceptibility to practical imperfections or external manipulation by a malicious adversary, which can compromise the quality of their output [8]. Additionally, it is hard to give a convincing argument for the randomness yielded by some of these devices, as many implementations simply rely on ignorance about the entropy source rather than intrinsic randomness. If the physical process measured is deterministic, such as the case of classical phenomena or a chaotic system, the final result is nonetheless still fundamentally predictable, and reasonable doubts about the randomness of the output can be posed [1]. In contrast to PRNGs, QRNGs explore the intrinsic probabilist nature of quantum phenomena as their source of randomness. Several implementations have been proposed, including generation schemes based on detection of radioactive decays [9, 10], but most schemes explore the proprieties of quantum optics through protocols, such as measurements of photon polarization states [11], amplified spontaneous emission [12, 13, 14], photonarrival times [15; 16; 17; 18], or phase noise from selected light sources [19; 20]. Recently, some fully integrated solutions have also materialized by employing photonic integrated circuits, which removes the need for bulky implementations [21; 22; 23; 24; 25; 26]. This is an important first step to reach mass deployment and allow these implementations to compete with the versatility shown by PRNGs. Unfortunately, further work is necessary to integrate all components into a single compact package, as customized designs and expensive electronic components are frequently the required trade-off. Furthermore, achieving a high-performance integrated randomness platform is technically challenging, as considerations, such as the presence of dark currents, or the responsivity and the bandwidth of the photodetectors significantly impact the generation rates achievable [25]. Perhaps one of the most promising and well-researched implementations employs homodyne measurements of the fluctuations of a vacuum-state as its entropy source, with several recent high-rate generation schemes being proposed [26; 27; 28; 29; 30; 31]. This approach offers high generation rates using a simpler setup than heterodyne-based QRNGs, can potentially be implemented with widely available technologies and shows high potential for on-chip integration due to the low number of components required. Furthermore, the vacuum state is easily obtained and can not be reproduced by an attacker, which provides resilience against external perturbations [27]. Despite this, several challenges are still present, such as assuring a good balancing condition or a significant quantum noise level, which can lead to the introduction of security loopholes [32].