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EPJ Quantum Technology

Correlation avoidance in single-photon detecting quantum random number generators by dead time overestimation

Balázs Solymos, Ágoston Schranz, Miklós Telek

Published Sep 19, 2024• 4 citations
Publisher

Abstract

Abstract In the case of quantum random number generators based on single photon arrivals, the physical properties of single-photon detectors, such as time-tagger clocks and dead time, influence the stochastic properties of the generated random numbers. This can lead to unwanted correlations among consecutive samples. We present a method based on extending the insensitive periods after photon detections. This method eliminates the unwanted stochastic effects at the cost of reduced generation speed. We calculate performance measures for our presented method and verify its correctness with computer simulations and measurements conducted on an experimental setup. Our algorithm has low complexity, making it convenient to implement in QRNG schemes, where the benefits of having uncorrelated output intervals exceed the disadvantages of the decreased rate.

DOI
10.1140/epjqt/s40507-024-00272-8

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Abstract In the case of quantum random number generators based on single photon arrivals, the physical properties of single-photon detectors, such as time-tagger clocks and dead time, influence the stochastic properties of the generated random numbers. This can lead to unwanted correlations among consecutive samples. We present a method based on extending the insensitive periods after photon detections. This method eliminates the unwanted stochastic effects at the cost of reduced generation speed. We calculate performance measures for our presented method and verify its correctness with computer simulations and measurements conducted on an experimental setup. Our algorithm has low complexity, making it convenient to implement in QRNG schemes, where the benefits of having uncorrelated output intervals exceed the disadvantages of the decreased rate.
A measurement-based validation of theoretical results on quantum random number generators (QRNGs) is considered in the paper. We have designed an experimental setup built around a single-photon detector to record random datasets of photon arrival time differences with various parameter settings. The collected datasets are used to generate random bit sequences with and without dead time overestimation. The statistical properties of the bit sequences are compared with analytical results on the one hand and assessed with four of the most popular statistical test suites on the other hand. The measurement results validate that the dead time overestimation algorithm helps to eliminate unwanted correlations from the generated bit sequences in practice.
We present a high-quality bias-free quantum random number generator (QRNG) using photon arrival time selectively, in accordance with the number of photon detection events within a sampling time interval in attenuated light. It is well shown in both theoretical analysis and experimental verification that this random number production method eliminates both bias and correlation perfectly without more postprocessing and that the random number can clearly pass the standard randomness tests. We fulfill theoretical analysis and experimental verification of the method whose rate can reach up to 45 Mb/s.
Quantum random number generators (QRNGs) produce true random numbers with significant applications in quantum communication and numerical computation, where high-rate random number generation is critical. Photon detection-based quantum random-number generation methods have been widely studied. However, the generation rate is constrained by the count rate of single-photon detectors. This study proposes an efficient method that enhances random number generation by simultaneously detecting photons in temporal and spatial dimensions. We achieved simultaneous detection of photon arrival time and spatial position by employing a laboratory-developed 5 × 5 single-photon detector array and a high-saturation count rate multichannel time-to-digital converter. The maximum efficiency of the method was 21.1 bits per event and it maintained a consistent efficiency of 17.6 bits per event while achieving a random number generation rate of 2.1 Gbps. The proposed QRNG approach offers a promising pathway for significantly increasing random number generation rates, benefiting applications that require secure and high-speed random number sequences.
This dissertation is the result of research which, although electrical and computer engineering in nature, also aims to improve the performance of many systems in the field of quantum information. For example, random number generators are used in almost all areas of science, and the initial portion of this work details the theory, design, and characterization of two photon-arrival-time quantum random number generators (QRNGs). After the QRNGs were completed, it was realized that their performance was severely limited both by the maximum detection rate of the single-photon detectors used, and the precision at which the arrival times could be resolved. The single-photon detectors used for both QRNGs are single-photon avalanche photodiodes (SPADs), devices which when operated below their breakdown voltage can create a macroscopic amount of current (an avalanche) in response to a single incident photon. Some of this charge can become trapped in defects or impurities; if this trapped charge is released when the SPAD is active, a secondary ‘false’ detection event, or ‘afterpulse’ can occur. To lower the afterpulse probability to reasonable levels (< 1%), we attempted to reduce the amount of avalanche charge by halting its growth promptly with high-speed electronics, so that defects have a lower probability of becoming populated in the first place. Initial results show reductions in afterpulse probability by up to a factor of 12, corresponding to a ~20% decrease in dead time, a value that could be improved further. We developed an FPGA-based time-to-digital converter system for use specifically with SPADs, achieving a time-bin resolution of 100 ps, with lower dead time and higher maximum detection rate than all currently available detection systems. This further allowed for the creation of a new higher-order SPAD characterization technique, which was identified previously unknown subtleties to SPAD operation. Finally, we developed an ultra-low-latency QRNG, which was used in one of the recent loophole-free demonstrations of quantum nonlocality. The final latency was below 2.5 ns, to our knowledge the lowest latency QRNG to date. Of special interest, however, is our subsequent exploration into the characterization of its bit-probability drift using atomic clock stability techniques. By employing the Allan deviation and implementing precision feedback, the additional frequency drift caused by environmental fluctuations is reduced such that the resulting bit stream can pass cryptographic random number tests for sample sizes up to 5 Gb. This system is currently intended for the NIST random-number beacon, a world-wide trusted source of random bits.
A quantum random number generation method based on measuring the time differences between photon detections is analyzed mathematically in terms of bit generation efficiency and bit generation rate. It was found that these two values cannot be maximized simultaneously by altering the incident photon rate of a light source with Poisson statistics, but the generation rate can be increased at the expense of efficiency. Analytical results are presented for both an idealized and a practical case. The detector’s dead time has been taken into consideration in the latter case, implying that, for certain combinations of the dead time and the measurement clock period, the generation rate becomes a two-peaked function of the incident photon rate. The theoretical results are confirmed by simulations, showing excellent agreement between the two.
A quantum random generator based on photon detection is here presented. The system consists of a source of photons, typically a commercial LED, coupled with a detector with single photon detection capability. The detector in this case is represented by a single pixel consisting of a SPAD and a time stamp circuit, which samples the arrival time of impinging photons within a predefined temporal window. The proposed implementation increases the efficiency of random bit extraction and reduces the afterpulsing probability, which can introduce undesirable correlation to the measurement. Preliminary results are reported, showing that the pixel has a flat behavior for a relevant range of intensity of the light, which makes the pixel robust against variations of external PVT parameters