Random numbers are needed in a number of applications, from computer simulations to data protection; basically, there are two types of generators of random numbers. The first type are pseudo-random number generators (PRNG), the software/hardware implementations of algorithms which produce random-looking sequences of numbers which by their algorithmic nature are not random but are rigorously proven to pass a number of statistical tests; or it is shown mathematically that to distinguish the produced sequences from truly random ones is an infeasible task since the task is polynomially equivalent to some hard mathematical problem for which no algorithms solving the problem in polynomial time are known. The second type of generators constitute the ones which derive random numbers from some physical processes which are believed to be chaotic and unpredictable by physical reasons. The latter generators are usually called true random number generators (TRNG). The only reason why the sequences of numbers produced by the latter generators are judged as random is that they pass standard batteries of statistical tests and (if a generator exploits some quantum system) by a reference to immanent randomness of quantum processes. However, in order to use a generator in sensitive applications, a mathematical evidence is needed. In the talk we discuss what kind of such an evidence can be obtained for quantum TRNG.
The talk is mostly based on the paper Vladimir Anashin. Free Choice in Quantum Theory: A $p$-adic View. Entropy 2023, 25(5), 830; https://doi.org/10.3390/e25050830