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Laser Physics Letters

On the limiting rate of generation of random sequences and the principle of particle identity

S. N. Molotkov

Published Jan 23, 2023• 5 citations
Publisher

Abstract

Abstract Estimates for the limiting rate of generation of random sequences in random number generators dictated by fundamental prohibitions of Nature are obtained. The relationship between the limiting rate of the generation of random sequences and the principle of particle identity is established.
DOI
10.1088/1612-202x/acb1af

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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.
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We present a simple approach to realize truly random number generator based on measuring the phase noise of a single-mode vertical cavity surface emitting laser. The true randomness of the quantum phase noise originates from the spontaneous emission of photons and the random bit generation rate is ultimately limited only by the laser linewidth. With the final bit generation rate of 20 Mbit/s, the truly random bit sequence guaranteed by the uncertainty principle of quantum mechanics passes the three standard randomness tests (ENT, Diehard, and NIST Statistical Test Suites). Moreover, a continuously generated random bit sequence, with length up to 14 Gbit, is verified by two additional criteria for its true randomness.