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Optical Engineering

Mathematical analysis of a quantum random number generator based on the time difference between photon detections

Ágoston Schranz, Eszter Udvary

Published Apr 8, 2020• 9 citations
Publisher

Abstract

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.

DOI
10.1117/1.oe.59.4.044104

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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.
Abstract A bit generation algorithm of a photon arrival times based quantum random number generator is proposed and investigated in terms of the quality of generated bits, bit generation efficiency and bit generation rate. The method's performance is analyzed mathematically, considering the properties of the physical equipment, such as discretized time measurement, inaccurate knowledge about the photon arrival rate and dead time. The proposed bit generation algorithm is also tested in a physical experiment.
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 an efficient and robust quantum random number generator based upon high-rate room temperature photon number detection. We employ an electric field-modulated silicon avalanche photodiode, a type of device particularly suited to high-rate photon number detection with excellent photon number resolution to detect, without an applied dead-time, up to 4 photons from the optical pulses emitted by a laser. By both measuring and modeling the response of the detector to the incident photons, we are able to determine the illumination conditions that achieve an optimal bit rate that we show is robust against variation in the photon flux. We extract random bits from the detected photon numbers with an efficiency of 99% corresponding to 1.97 bits per detected photon number yielding a bit rate of 143 Mbit/s, and verify that the extracted bits pass stringent statistical tests for randomness. Our scheme is highly scalable and has the potential of multi-Gbit/s bit rates.
The bit generation algorithm of a quantum random number generator based on photon arrival time differences is improved in terms of the bit generation efficiency and bit generation rate. The method is analyzed mathematically, proving that, in theory, the improved generator still produces random numbers of high quality without the need of resorting to postprocessing algorithms. The effects of nonidealities are quantitatively analyzed to provide bounds for the maximum tolerable deviations from uniformity. Experimental investigations are conducted on a prototype, showing that the method is capable of increasing the rate of bit generation by more than 47% on the same physical architecture.
Abstract The performance analysis of a quantum random number generator (QRNG), operating based on the interarrival time differences between consecutive photon detections from a coherent light source, is presented. The proposed analysis approach accurately takes into account the physical properties of the single‐photon detection systems, such as discretised time measurement, the correlations induced by the asynchronous arrival of photons with respect to the time resolution grid, and the dead time after observations and provides the QRNG's relevant performance measures, such as the joint distribution of bits, lag‐ r correlations, the bit generation overhead and the bit generation time. Analysis results are verified by computer simulations.
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.