Source-linked AI summary
A bias-free quantum random number generation using photon arrival time selectively
Jian-min Wang, Tian-yu Xie, Hong-fei Zhang, Dong-xu Yang, Chao Xie, Jian Wang
TL;DR
Physical true random numbers are increasingly needed for quantum applications because quantum processes are theoretically unpredictable. This paper develops a bias-free QRNG based on selective photon arrival times and reports a rate up to 45Mbps without additional post-processing.
Problem
Quantum applications increasingly require physical true random numbers beyond deterministic pseudo-random numbers.
Method
The paper selects photon arrival times according to the number of detection events within each sampling interval to generate quantum random numbers without additional post-processing.
Results
45Mbps random-number generation was achieved, with min-entropy H∞=0.99946 derived from the biggest frequency 0.003918.
Takeaways & Limitations
The scheme produces high-quality bias-free random numbers without additional post-processing and can pass prevalent randomness tests.
Takeaways & Limitations
The method is constrained by detector dead time and by fused multiple detections when intervals between detections are shorter than td, causing deviation from theory.
Abstract
from arXiv · showhide
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 showed in both theoretical analysis and experiments verification that this random number production method eliminates both bias and correlation perfectly without more post processing and 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 45Mbps.
1. Introduction
Quantum processes provide physical true random numbers needed by emerging applications such as quantum cryptography. The paper proposes a bias-free photon-arrival-time scheme reaching up to 45Mbps without additional post-processing.
- Quantum processes are theoretically unpredictable, making them a source of physical true random numbers.
- Optical-field approaches offer controllable detection and higher photon density than nuclear-decay methods, supporting higher entropy and rates.
- 45Mbps: the demonstrated scheme generates bias-free random numbers by selectively using photon arrival times without additional post-processing.
2. SETUP AND THEORY ANALYSIS
The method models photon detections as a Poissonian process, digitizes arrival times into bins, and retains intervals containing only one detected pulse. Dead time is analyzed because pulse merging can make the retained distribution deviate from the ideal theory.
- Experimental setup: The setup attenuates LED light to the single-photon level, detects pulses with a PMT, and uses TDC-FPGA processing to select one-pulse periods and output arrival times.The discriminator converts amplified PMT pulses into digital signals before arrival-time measurement and FPGA selection.
- Poissonian model: Photon detections are modeled as independent events following a Poissonian distribution with mean event rate λ.
- Time digitization: The digitized arrival-time variable uses least-significant-bit bins of size t0 over an observed period T0, with N0=T0/t0 bins.The direct arrival-time distribution is exponential rather than uniform, motivating the selective procedure.
- Selective sampling: Retaining periods with exactly one detection makes every time-bin probability uniform under the Poissonian model.
- Dead-time analysis: Dead time td can merge nearby detections into one pulse, so the analysis accounts for preceding dead-time intervals and multi-detection pulses.The calculation includes one-, two-, and three-detection contributions, with higher-order effects described as minute at the single-photon level.
3. EXPERIMENTS AND RESULTS
The experiment compares measured arrival-time distributions with theory and evaluates bitrate, min-entropy, and data retention. After truncation, the measured distribution agrees with theory, achieves high min-entropy, and supports rates up to 45Mbps.
- Experimental setup: 0.162ns TDC precision and 5ns PMT pulses yield an observed period T0=51.84ns, with experimental and theoretical values plotted together.The observed period is calculated as T0=320×0.162ns=51.84ns.
- Experimental setup: Fig.3 shows good agreement between experimental data and the theoretical prediction based on Eq. (10).The theory is shown as a red solid line and the measurements as green dots.
- Randomness evaluation: 0.999996 min-entropy is obtained after cutting off Nd on both sides and renormalizing the remaining distribution.The corresponding remaining proportion is approximately 0.803, or 256/320.
- Bitrate and utilization: 45Mbps is reached under continuously improved illumination intensity, and the generated numbers pass prevalent randomness tests.A calculated bitrate of approximately 22.13Mbps agrees with the experimental value.
- Randomness evaluation: 0.99946 real min-entropy is derived from the measured maximum frequency 0.003918, while device imperfections prevent the ideal level.The paper attributes the gap to device imperfections, especially TDC counting loss.
- Bitrate and utilization: More than 0.8 of the raw sequence remains after rejecting periods with more than one detection, indicating high raw-data utilization.The bitrate depends directly on T0, P(X=1), td, and t0; td and t0 are determined by device performance.
- Bitrate and utilization: The uniform distribution after truncation depends little on illumination intensity, producing steady random-number quality during the experiment.This reduces sensitivity to minute illumination drift compared with the cited alternative scheme.
4. RANDOMNESS TESTS
The QRNG was evaluated with STS and DieHard test suites, with p-values routinely above the significance level without post-processing. Analysis of about 100GB found no evident defects, supporting the reported quality and reliability of the generated random numbers.
- STS and DieHard tests produced p-values routinely above the significance level without post-processing.STS analyzed 1Mbit × 1000, while DieHard used the same operating parameters and quantity as before.
- About 100GB of generated data were analyzed across the experimental processes, with no evident defects found.
- The authors conclude that the tested scheme provides high-quality, reliable, ready-for-use random numbers.The conclusion also states that the method transforms an exponential distribution into a desirable uniform distribution and is nonparametric.