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Journal of Experimental and Theoretical Physics Letters

Implementation of a Quantum Generator of Random Numbers: Extraction of Provably Random Bit Sequences from Correlated Markov Chains

Kirill A. Balygin, S. P. Kulik, S. N. Molotkov

Published Apr 1, 2024• 6 citations
Publisher

Abstract

An experimental implementation of a quantum random number generator has been proposed. A new method for the extraction of provably random bit sequences from correlated sequences of photocounts, which are Markov chains, has been implemented experimentally for the first time. The reached generation rate of bits 0 and 1 is 154.5 Mbit/s. Fundamental natural constraints on the achievement of perfect true randomness are also discussed.

DOI
10.1134/s0021364024600575

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An experimental implementation of a quantum random number generator has been proposed. A new method for the extraction of provably random bit sequences from correlated sequences of photocounts, which are Markov chains, has been implemented experimentally for the first time. The reached generation rate of bits 0 and 1 is 154.5 Mbit/s. Fundamental natural constraints on the achievement of perfect true randomness are also discussed.
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.
One of the main problems in the construction of quantum random number generators Ð obtainment of a provably random output sequence from physical measurements, i.e., from an initial sequence generated by a physical random number generator Ð is investigated.The conceptual feasibility and the conditions under which randomness can be `reached,' as well as the meaning of the `provable randomness' term, are discussed.We consider the methods of extracting provably random bit sequences from stationary Markov chains of finite order, i.e., under the assumption of the finite depth of the dependence of the results of physical measurements on the prehistory, which is an adequate approximation of the real situation.The extraction of the output provably random bit sequence from the initial sequence of the results of physical measurements using V F Babkin's effective arithmetic coding method is demonstrated.It is shown that random bit sequences can be provably obtained even from primary sequences of the results of physical measurements, which are dependent on (correlated to) any finite depth (prehistory).We aim to reveal the connection of various approximations employed in the development and description of methods for obtaining random bit sequences with the basic physical limitations of Nature.The mathematical proofs are detailed to the level of practical algorithms applied in real random number generators.The necessary mathematical propositions are presented at an intuitive level for physicists, do not require prior knowledge in this area, and are comprehensible to undergraduate university students.
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.
Квантовые генераторы случайных чисел, экстракция доказуемо случайных битовых последовательностей РёР· траекторий цепи Маркова, Арбеков Р