Extraction of quantum randomness

The nature of randomness and constructive and provable methods to obtain (extract) it from observations of physical systems are discussed. True randomness, which exists only in a microcosm in the quantum-mechanical description of physical systems, is a fundamental property of quantum systems, which manifests itself in the outcomes of measurements upon quantum systems. The classical description of physical systems does not include any randomness and, in fact, it is introduced ‘manually’ by means of uncertainty—unknown initial conditions. Methods to really ‘feel’ quantum randomness are discussed using the example of a quantum device, a random number generator. Issues related to the ‘proof’ of randomness—testing of numerical sequences—are reviewed, and logical constructions that underlie such testing are analyzed. A mathematical apparatus is used to this end, which does not require special academic training, so standard knowledge from university courses on quantum mechanics and probability theory is sufficient. The authors aim to track a unified logical path from the origin of randomness in the quantum domain to its extraction, physical implementation, and testing.