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Journal of Experimental and Theoretical Physics

The Fundamental Limit of the Random Sequence Generation Rate in Quantum Generators with a Continuous Variable

S. N. Molotkov

Published Mar 1, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776120020065

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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.
Nowadays information technologies are widespread and used in every computer-based system, hence information security tasks are quite important and their successful solution is required in business process. Cryptographic means are used in different applications, especially in cases when data confidentiality should be provided; although they can be utilized to maintain data availability and integrity, user's anonymity, author's non-repudiation and so on. Many information security tools use random numbers, but unfortunately, quality of output random numbers and speed of their generation do not satisfy modern requirements. The rate of production-run random number generators is limited by the physical processes used. One of the reasons of low random numbers generating rate is application of binary events. Many generators use analog events, e.g. noise in electronic devices, converted to binary numbers utilizing the threshold value or quantum discrete events, e.g. photon passing through the polarizer. The main idea of this work is that one can increase random number generator's rate using the non-binary sequences, e.g. non-binary quantum processes.
Quantum random number generators (QRNGs) produce true random numbers based on the inherent randomness of quantum theory, rendering them a foundational segment of quantum cryptography. Distinguished from trusted-device QRNGs whose security depends on characterized devices, semi-device-independent (semi-DI) QRNGs permit partial devices to be defective or even maliciously manipulated, which achieves a good trade-off between generation rate and security. In this paper, we propose a semi-DI QRNG that resists general attacks while accounting for finite-size effects. The protocol requires no rigorous characterization of the source and measurement devices other than limiting the energy of the emitted states, significantly reducing the demands on practical QRNG systems. Leveraging the tight Kato inequality for correlated variables, we show that our protocol generates more randomness than it consumes. Furthermore, we demonstrate the scheme on a continuous-variable system with ternary inputs of states. Heterodyne detection is employed to enable phase compensation through data postprocessing, alleviating the stringent requirement on system stability. The system operates at 100 MHz, achieving a net random number generation rate of 1.165 Mbps at 5.3x10^9 rounds. Our work offers a promising approach to achieve both the robust security and high generation rate with a simple experimental setup.
Quantum random number generators (QRNG) have important applications in cryptographic protocols, gaming and lotteries, among others. In contrast to pseudo-random number generators based on software, the sequence of random numbers generated is truly random. Most QRNG found in the literature are based on optoelectronic devices like single-photon sources and single-photon detectors. In this direction, the present dissertation deals with the theory and experiment QRNG based photonic systems, taking into account QRNG using discrete and continuous variables. In particular, three issues were considered: 1) a new model of continuous variable QRNG based on light polarization was proposed. 2) The performance of a QRNG employing only one single-photon detector, taking into account the afterpulsing and the quantum light state used, coherent or thermal, was realized. 3) A QRNG with binomial distribution was built.
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.