Ability to generate random numbers is an important resource for many applications ranging from scientific research to practical cryptography and quantum technologies. However, a widely accepted definition of random numbers, or randomness, has eluded researchers thus far. Without a definition, it is impossible to complete security proofs or make new industrial standards. Here, we propose an information-theory-based definition of randomness which, unlike state of the art, does not try to find desirable properties of generated numbers, but rather focus on the physical process of random number generation. We explain its intuitiveness, demonstrate its verifiability and further define randomness deviation as a measure of quality of the random number generating process or device.

翻译：随机数生成能力是众多应用的重要资源，涵盖从科学研究到实际密码学及量子技术等领域。然而，迄今为止，研究人员尚未形成被广泛接受的随机数或随机性定义。缺乏这一定义，将无法完成安全性证明或制定新的工业标准。本文提出一种基于信息论的随机性定义，与现有定义不同，该定义并不试图寻找生成数值的理想特性，而是聚焦于随机数生成的物理过程。我们阐释了其直观性，论证了其可验证性，并进一步定义随机性偏差作为随机数生成过程或装置的质量度量指标。