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True random numbers from amplified quantum vacuum
M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, V. Pruneri
TL;DR
Existing random-number methods include fast pseudo-random algorithms and quantum generators, but high-rate true randomness from vacuum fluctuations remains challenging to measure efficiently. This paper uses optical amplification and interferometry to convert vacuum fluctuations into random bits, demonstrating a 1.11 Gbps QRNG with commercially available components. The device is reported as extendable beyond 10 Gbps and potentially to 100 Gbps.
Problem
Vacuum fluctuations can provide many broadband true random bits, but direct recording requires shot-noise-limited detectors and can reduce bandwidth.
Method
The method strongly attenuates the laser cavity field, amplifies vacuum-derived fluctuations, and uses interferometry and hashing to extract secure random bits.
Results
1.11 Gbps is obtained as the random bit generation rate after cryptographic extraction, using commercially available optical components.
Takeaways & Limitations
The demonstrated high-bandwidth vacuum-based QRNG is low power, robust, automatable, and potentially applicable to secure communication and cryptography.
Takeaways & Limitations
Raw data can contain detectable patterns from classical noise, so cryptographic hashing is required to remove that information before output.
Abstract
from arXiv · showhide
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.
1 Introduction
Quantum random number generators use intrinsic quantum randomness, while vacuum fluctuations offer a broadband source capable of yielding many true random bits per measurement. The paper proposes optical amplification to extract random bits from vacuum while addressing practical speed, cost, robustness, and detector constraints.
- Secure communications, numerical simulation, and quantitative finance rely on random numbers.
- QRNGs generate true random numbers from randomness embedded in quantum physics, unlike pseudo-random algorithms.
- Vacuum fluctuations are attractive because continuous electric-field measurements can yield many true random bits and are broadband, white, and uncorrelated.
- Ensuring that measured fluctuations originate from true vacuum is difficult because scattered light adds a non-random field component.
- Optical amplification with strong current modulation provides vacuum-based randomness, short coherence time, high signal level, and several random bits per detection event.
2 Device operation
The device uses a directly modulated DFB laser and an all-fiber unbalanced Mach–Zehnder interferometer to generate and overlap phase-randomized pulses. Commercial optical components, controlled path delay, and fast photodetection support the measurement of their interference.
- A DFB laser diode is directly modulated near 100 MHz with approximately 1 ns electrical pulses.
- A polarization-maintaining all-fiber unbalanced Mach–Zehnder interferometer with approximately 10 ns relative delay provides stable single-mode operation.
- The laser operates at 25 mA, below its 36 mA threshold, producing phase-randomized 400 ps optical pulses with 3.5 mW peak power.
- A polarization-maintaining coupler splits each pulse into two interferometer arms, while a second coupler recombines the delayed pulses for interference.
- A 150 MHz photodiode and a 200 MHz-bandwidth oscilloscope collect and process the interfering optical pulses.
- The path delay is adjustable so subsequent pulses temporally overlap, including through temperature-dependent changes in fiber propagation.
3 Laser physics analysis
The laser first attenuates its cavity field below threshold, allowing amplified spontaneous emission to replace prior coherence with a random phase, then amplifies the equilibrated field above threshold. The analysis shows strong attenuation can suppress pulse memory sufficiently for rates above 100 Gbps in principle.
- Below threshold, strong attenuation and amplified spontaneous emission reduce prior coherence and introduce a true random phase from vacuum fluctuations.
- Above threshold, phase-insensitive amplification increases the equilibrated field while gain depletion limits the output amplitude.
- The amplified output reaches approximately 3.5 mW, or 1.5 × 10^7 photons/ns, with about 3 × 10^5 photons in the cavity.
- At 20 GHz modulation, approximately 0.25 ns attenuation produces 100 dB attenuation, leaving a previous-pulse contribution about 15 bits below vacuum fluctuations.
- The analyzed process can support QRNG rates exceeding 100 Gbps.
4 Characterization of the coherence of the laser pulses
Interferometric measurements characterize pulse-energy distributions, coherence, and phase relations between successive pulses. The results show high interference visibility and statistically identical behavior whether the interferometer phase is fixed or swept.
- The interferometer output combines the current pulse with a delayed pulse, enabling first-order coherence measurements through correlation functions.
- Pulse energies are expected to be narrowly distributed, while successive pulses have similar envelopes and random phases.
- Interference broadens the output distribution most when the interferometer delay equals the pulse repetition interval.
- The measured interference visibility is approximately 90.22%.
- Statistics are identical for fixed and swept interferometer phase, indicating no phase relation between successive pulses.
5 Statistical testing
The study characterizes pulse statistics, correlations, and entropy to assess the randomness of the acquired data. Classical-noise patterns are addressed by cryptographic extraction, which reduces the raw-bit output by a factor of 1.08.
- Data acquisition: 25 samples over a pulse were acquired and converted into a single measurement using a 200 MHz oscilloscope and 12-bit ADC.The oscilloscope sampled at 2.5 Gsps over a 10 ns range, while the photodiode output was highpass filtered at 40 MHz.
- Distribution analysis: The pulse-energy distribution was measured under different pulse-repetition frequencies and loop-temperature conditions, with no observable phase effect on the distribution.The reported absence of a loop-phase effect indicates statistical independence of the pulses’ phases.
- Correlation analysis: 106 output pulses were collected to characterize raw-data correlations and determine extractable random bits per pulse.The normalized correlation of successive samples showed delta-function-like behavior, indicating a random sequence.
- Randomness extraction: Classical noise can contain detectable patterns even when it appears random, so its entropy provides an upper bound on the information it contributes.This motivates removing the classical-noise contribution from the combined quantum and classical noise before extraction.
- Entropy analysis: Entropy was calculated from the measured distribution by dividing it into 2b equally sized bins and computing Shannon entropy.The optical contribution was reported as up to 11.1 bits per pulse after subtracting entropy associated with the relevant contribution.
- Randomness extraction: Cryptographic hashing was used to remove classical-noise information, with a raw-bit reduction factor of 1.08.The Whirlpool hash function was used, although other standard randomness extractors could also have been employed.
6 Conclusions
The work demonstrates high-bandwidth extraction of true random bits from quantum vacuum fluctuations using optical amplification. Commercially available components achieved over 1 Gbps, while the authors indicate that higher rates may be possible with suitable laser and telecommunications hardware.
- Conclusions: Optical amplification extracts random bits from quantum vacuum fluctuations while strong attenuation ensures that the signal originates from quantum noise.The amplification also produces macroscopic signals compatible with high-bandwidth detection.
- Conclusions: Over 1 Gbps true random number generation was demonstrated using commercially available components.The device is described as low power, robust, and amenable to automation for long operational lifetimes.
- Conclusions: Rates above 10 Gbps and even 100 Gbps are considered possible based on laser-physics considerations.The proposed extension relies on high-speed modulation sources and detectors associated with optical-fiber telecommunications.