Various methods for the clustering of photocounts constituting a sequence of random numbers are considered. It is shown that the clustering of photocounts resulting in the Fermi–Dirac distribution makes it possible to achieve the theoretical limit of the random number generation rate.
To implement quantum random number generators, it is fundamentally important to have a mathematically provable and experimentally testable process of measurements of a system from which an initial random sequence is generated. This makes sure that randomness indeed has a quantum nature. A quantum random number generator has been implemented with the use of the detection of quasi-single-photon radiation by a silicon photomultiplier (SiPM) matrix, which makes it possible to reliably reach the Poisson statistics of photocounts. The choice and use of the optimal clustering of photocounts for the initial sequence of photodetection events and a method of extraction of a random sequence of 0’s and 1’s, which is polynomial in the length of the sequence, have made it possible to reach a yield rate of 64 Mbit/s of the output certainly random sequence.
A quantum random number generator is experimentally realized. The initial randomness source is a sequence of photocounts from quasi-single-photon radiation detected with a SiPM (Silicon Photo Multiplier) silicon avalanche detector array. The use of a SiPM provides a reliable control of the quantum nature of the Poisson photocount statistics. A special algorithm with nonexponential complexity allows one to extract from the Poisson process all the randomness contained in it, namely, a random uniform sequence of 0 and 1.
Abstract 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.
The possibility of using avalanche photodiodes that operate in the single-photon registration mode as a source of a random physical quantity in generators of random number sequences was evaluated. The operating modes of avalanche photodiodes were determined that allow generation of streams of random events, whose statistical characteristics are similar to those of a Poisson stream. Estimates of the similarity of the properties of generated random binary sequences to the properties of a uniformly distributed sequence are presented.