Optical fibre-based quantum random number generator: stochastic modelling and measurements.

In this work, we present a study of a quantum random number generation system based on a branching path approach with spatial superposition principle, realised using fibre optics. The analysis of the experimental system was supported by the development of a stochastic model of the entropy source, which, to the best of the authors' knowledge, has not yet been properly described. This resulted in the analytical equations for the probability of possible output quantum states depending on the initial properties of the system. Based on the presented model, the quantum efficiency and the Shannon entropy were calculated and compared with experimentally obtained values, which resulted in full agreement between these data. Additional statistical tests were performed on random numbers obtained theoretically and experimentally to confirm their high degree of randomness and their usability in cryptographic applications. The fact that the developed system is based on fibre optics allows it to operate in stable conditions with a final efficiency at the level of 15%, which provides a random number generation rate of about 8 kb/s. The developed system is used as an input to the quantum key distribution system, which has possible applications in cryptography or military and commercial secure communications.