Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Доклады Российской академии наук Математика информатика процессы управления / Doklady Mathematics

ON THE EXTRACTION OF RANDOM BIT SEQUENCES IN QUANTUM RANDOM NUMBER GENERATORS WITH SEVERAL INDEPENDENT MARKOV SOURCES

I. M Arbekov, S. N Molotkov

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The paper presents a method for extracting provably random bit sequences from several independent trajectories of circuits Markov, each of which has an arbitrary finite order. The combined use of several trajectories makes it possible in practice, when implementing quantum randomnumber generators, to significantly increase the speed of generating output bit sequences.

DOI
10.7868/s3034504925010026

Related papers

On the Extraction of Random Bit Sequences in Quantum Random Number Generators with Several Independent Markov Sources

Igor M. Arbekov, S. N. Molotkov

Abstract The paper presents a method for extracting provably random bit sequences from several independent Markov chain trajectories, each having an arbitrary finite order. In implementing quantum random number generators, the combined use of several trajectories makes it possible to significantly increase the speed of generating output bit sequences.

Doklady Mathematics•Feb 1, 2025•0 citations

Quantum random number generators, extraction of provably random bit sequences from Markov chain trajectories

Igor M. Arbekov, S. N. Molotkov

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.

Physics-Uspekhi•Feb 1, 2024•4 citations

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

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.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 2024•6 citations

Quantum random number generators, extraction of provably random bit sequences from Markov chain trajectories

Igor M. Arbekov, S. N. Molotkov

Квантовые генераторы случайных чисел, экстракция доказуемо случайных битовых последовательностей РёР· траекторий цепи Маркова, Арбеков Р

Uspekhi Fizicheskih Nauk•Feb 1, 2024•3 citations

A Novel Hybrid Method for Randomness Extraction

Maksim Iavich, Роман Сергійович Одарченко

Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.

CRC Press eBooks•May 30, 2025•0 citations

Source-Independent Quantum Random Number Generation

Zhu Cao, Hongyi Zhou, Xiao Yuan +1 more

Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics.In general, a physical generator contains two parts-a randomness source and its readout.The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness.However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output.To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted.In our randomness analysis, we make no assumptions about the dimension of the source.For instance, multiphoton emissions are allowed in optical implementations.Our analysis takes into account the finite-key effect with the composable security definition.In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit.In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 × 10 3 bit=s.

arXiv:1508.04880•Physical Review X•Feb 25, 2016•153 citations
The paper presents a method for extracting provably random bit sequences from several independent trajectories of circuits Markov, each of which has an arbitrary finite order. The combined use of several trajectories makes it possible in practice, when implementing quantum randomnumber generators, to significantly increase the speed of generating output bit sequences.
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.
Квантовые генераторы случайных чисел, экстракция доказуемо случайных битовых последовательностей РёР· траекторий цепи Маркова, Арбеков Р
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics.In general, a physical generator contains two parts-a randomness source and its readout.The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness.However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output.To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted.In our randomness analysis, we make no assumptions about the dimension of the source.For instance, multiphoton emissions are allowed in optical implementations.Our analysis takes into account the finite-key effect with the composable security definition.In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit.In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 × 10 3 bit=s.