The Fundamental Limit of the Random Sequence Generation Rate in Quantum Generators with a Continuous Variable

A fundamental constraint on the generation rate in quantum random number generators with a continuous variable is obtained by minimal mathematical means. This constraint is valid for any signal intensity—any number of photons in a quantum state. For large occupation numbers, the random number generation rate increases logarithmically with the number of photons, but always remains finite. For a small number of photons, the generation rate is proportional to the number of photons. For any number of photons, the limiting random number generation rate is proportional to the frequency band of the signal—a quantum state.