Quantum generators of random numbers

Marcin M Jacak,Janusz E Jacak,Piotr Jóźwiak,Jakub Niemczuk

doi:10.1038/s41598-021-95388-7

Abstract

Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.

Highlights

Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, and mathematical modeling, Monte Carlo methods, gambling and many others
We emphasize the key role of the unconditional randomness of quantum random number generators in contrast to pseudorandom classical generators
We identify quantum ideal sources of entropy in the randomness of quantum measurements according to the von Neumann scheme, and innovatively in quantum transitions based on the so-called Fermi golden rule

Summary

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It is difficult to notice significant differences between the two generators (quantum and pseudorandom) in the analysis of the NIST STS results, which may indicate the fact that during the statistical testing of random sequences it is not possible to detect true randomness. The above examples demonstrated that the NIST’s test is too weak to distinguish between pseudorandom classical sequence and true quantum random sequence, at least at the tested sequence length of 100 MB. This test was able to detect a bias, . Application of the simple von Neumann algorithm (it considers two bits at a time (non-overlapping), taking one of three actions: when two successive bits are equal, they are discarded; a sequence of 1,0 becomes

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Conclusion