Demonstration of quantum random number generation using nitrogen vacancy centres

This paper presents an experimental demonstration of high-speed quantum random number generation using nitrogen vacancy centers in fluorescent nanodiamonds, achieving generation rates up to 4.77 Mbits/s that pass standard statistical tests without post-processing and offer a compact on-chip solution.

The Gist

The Big Idea: Making True Randomness from Tiny Diamonds

Imagine you need to pick a number for a lottery, but you don't want anyone to be able to guess it. On a normal computer, "random" numbers are actually just clever tricks. They follow a secret recipe (a formula) that starts with a seed number. If you know the recipe and the seed, you can predict the next number. It's like a magician who always pulls the same rabbit out of the same hat because they practiced the trick.

This paper is about building a machine that doesn't use tricks. Instead, it uses the fundamental laws of the universe—specifically, the fact that nature is truly unpredictable at the smallest scale—to generate numbers that no one can ever predict.

The Magic Tool: "Artificial Atoms" in Diamonds

The researchers used tiny specks of diamond, called nanodiamonds. Inside these diamonds are tiny defects called Nitrogen-Vacancy (NV) centers. Think of these defects as "artificial atoms" trapped inside the diamond.

When you shine a green laser light on these defects, they get excited and then immediately relax, popping out a single particle of light called a photon.

• The Analogy: Imagine a popcorn kernel. When you heat it (the laser), it pops (emits a photon). The exact moment it pops is completely random. You can't predict if it will pop at 1.00 seconds or 1.000001 seconds. That split-second timing is the source of the randomness.

The Experiment: Catching the Pops

The team set up a high-tech microscope to shine a laser on these nanodiamonds and catch the photons as they popped out. They tested five different "regions" on their sample:

1. Region 1: A single diamond with just one NV center (one popcorn kernel).
2. Region 2: A diamond with two NV centers.
3. Region 3: A diamond with four NV centers.
4. Region 4: A cluster of diamonds with about 17 NV centers.
5. Region 5: A big cluster with just under 50 NV centers.

How They Turned Time into Numbers

They used a method called the "Time-of-Arrival" scheme.

• The Analogy: Imagine a clock that ticks very fast. Every time the clock ticks, it resets. The researchers divided each tick into 256 tiny slices (like cutting a pie into 256 pieces).
• When a photon arrives, the researchers check which "slice" of the tick it landed in.
• If it lands in slice #1, that's a specific number. If it lands in slice #256, that's a different number.
• Because the photon's arrival time is truly random, the slice it lands in is also truly random.

The Results: Speed and Quality

The paper reports two main achievements:

1. Speed (The Generation Rate)

• With just one NV center, they generated random numbers at a speed of 0.173 million bits per second.
• With the big cluster (Region 5) containing nearly 50 NV centers, the speed jumped to 4.77 million bits per second.
• The Comparison: This is a massive improvement. Previous experiments using similar diamond defects were much slower (some were only thousands of bits per second). By using a cluster of centers, they made the process about 10 times faster than the best previous attempts with this specific technology.

2. Quality (The "True Randomness" Test)

• Sometimes, random generators have a slight "bias" (like a coin that lands on heads 51% of the time). To fix this, computers usually have to do extra math to clean up the data.
• The Finding: The researchers found that their numbers were so perfectly random that they passed the strictest industry tests (called ENT and NIST tests) without needing any cleanup.
• The Analogy: It's like rolling a die and getting a perfectly fair result every single time, so you don't need to throw away the "bad" rolls. The raw data was already perfect.

Why This Matters (According to the Paper)

The paper concludes that this setup is a robust way to make high-quality random numbers.

• Compactness: Because nanodiamonds are tiny, this technology could eventually be built onto a small computer chip (on-chip).
• Security: Since the randomness comes from nature itself, it is much harder to hack or predict than the "fake" random numbers used in standard software.

Summary

The researchers proved that by shining a laser on tiny defects in diamonds and timing exactly when the light particles pop out, they can create a stream of numbers that is truly unpredictable. By using a cluster of these defects, they made the process fast enough to be useful for real-world applications, all without needing to do complex math to fix the numbers afterward.

Technical Summary

1. Problem Statement

Random numbers are critical for cryptography and Monte Carlo simulations. However, classical pseudorandom number generators (PRNGs) are deterministic and can be predicted by machine learning algorithms, posing security risks. While Quantum Random Number Generators (QRNGs) offer true unpredictability based on quantum mechanics, existing implementations face trade-offs:

• Bulkiness: Early QRNGs using radioactive decay were large and slow.
• Complexity/Speed: Photonic QRNGs based on "branching paths" (beam splitters) are robust but suffer from lower generation rates because they typically extract only one bit per photon.
• Post-processing: Many schemes require complex randomness extraction or post-processing to remove bias, which reduces the final generation rate.
• Source Limitations: Previous QRNGs using Nitrogen-Vacancy (NV) centers in diamond were limited to the branching paths scheme, resulting in low generation rates (e.g., < 1 Mbit/s).

The authors aim to demonstrate a time-of-arrival (ToA) QRNG scheme using NV centers in fluorescent nanodiamonds. This approach promises higher speeds, simpler hardware (source + detector only), and the ability to generate high-quality random numbers without post-processing.

2. Methodology

Experimental Setup

The researchers utilized a laser-scanning confocal microscopy setup to excite NV centers in fluorescent nanodiamonds and collect emitted photons.

• Excitation: A continuous-wave (CW) green laser (532 nm) was used to drive NV centers from the ground state to an excited state.
• Sample: Fluorescent nanodiamonds (approx. 40 nm diameter) were spin-coated onto a glass coverslip. The sample contained regions with varying numbers of NV centers (from single centers to clusters of ~50).
• Detection: Emitted photons (fluorescence > 567 nm) were collected, filtered (600–800 nm), and directed to a Single-Photon Avalanche Diode (SPAD).
• Timing: A PicoQuant TimeHarp 260 PICO time-to-digital converter recorded photon arrival times with 25 ps precision.

The Time-of-Arrival (ToA) Scheme

Unlike branching path schemes, the ToA scheme generates random numbers based on when a photon arrives relative to an external clock.

• The time axis is divided into periodic intervals of length $T$.
• Each interval is subdivided into $M$ bins (where $M=256$, yielding 8 bits per photon).
• The index of the bin in which a photon arrives constitutes the random number.
• Key Constraint: The interval $T$ (12.8 ns) was set to be shorter than the detector's dead time (24 ns) to ensure at most one photon is registered per interval, satisfying the condition for uniform distribution.

Characterization

Before QRNG generation, the authors characterized five specific regions of interest (R1–R5) on the sample:

1. Fluorescence Scanning: To locate nanodiamonds.
2. Second-Order Correlation ($g^{(2)}(\tau)$): Measured using a Hanbury Brown and Twiss interferometer to determine the number of NV centers ($N$) in each region.
   • R1: 1 NV center.
   • R2: 2 NV centers.
   • R3: 4 NV centers.
   • R4: ~17 NV centers.
   • R5: ~49 NV centers.
3. Spectral Analysis: Used to distinguish between neutral ($NV^0$) and negatively charged ($NV^-$) centers.

3. Key Contributions

1. First ToA QRNG with NV Centers: This is the first experimental demonstration of the time-of-arrival QRNG scheme using single photons emitted by NV centers in nanodiamonds. Previous NV-based QRNGs relied on the branching paths scheme.
2. Theoretical Framework for Multi-Photon Emitters: The authors derived a theoretical model for the min-entropy of a ToA scheme using $N$ independent single-photon emitters with background contamination. They generalized the theory from a single emitter to multiple emitters, accounting for multi-photon emission events within the time bin.
3. High-Rate, Post-Processing-Free Generation: The study demonstrates that by utilizing clusters of NV centers, the generation rate can be significantly increased while maintaining high randomness quality that passes industry-standard tests without any randomness extraction or post-processing.
4. Scalability Analysis: The work provides a roadmap for scaling QRNG rates on-chip by increasing the number of emitters, showing that even with multi-photon contamination, the statistical quality remains high.

4. Results

Generation Rates

The random number generation rates increased significantly with the number of NV centers:

• Single NV Center (R1): 0.173 Mbits/s.
• ~50 NV Centers (R5): 4.77 Mbits/s.
• Comparison: The rate of 4.77 Mbits/s represents an order of magnitude improvement over the highest previously reported rate for NV-center QRNGs (0.76 Mbits/s using branching paths).

Statistical Quality

• Min-Entropy: Theoretical analysis showed the min-entropy ($H_\infty$) is extremely close to the ideal value of 1.0 bit per bit for all regions (e.g., 0.999975 for R1, 0.999314 for R5).
• Statistical Tests: 800 Mbit samples from all five regions passed:
  • ENT Test Suite: Including entropy, chi-square, arithmetic mean, and serial correlation tests.
  • NIST Statistical Test Suite: Specifically designed for cryptographic applications.
• Uniformity: The relative frequency of 0s and 1s was approximately 0.5 for all regions.
• Correlation: Pearson correlation coefficients for delays up to 15 bits were near zero, indicating no serial correlation.

Comparison with Previous Work

The current implementation outperforms previous NV-center QRNGs in speed by a factor of ~60 (compared to 34.37 bits/s) and ~6x (compared to 0.76 Mbits/s), while eliminating the need for post-processing (unlike many other high-speed schemes that require hashing).

5. Significance

• Robust On-Chip Potential: The simplicity of the ToA scheme (requiring only a source and a detector) makes it highly suitable for integration into compact, on-chip quantum devices. The authors note that future integration with on-chip electrical excitation and detection could lead to highly robust, moderate-speed QRNG chips.
• Practical Cryptography: The ability to generate cryptographically secure random numbers at multi-Mbit/s rates without complex post-processing is a significant step toward practical, high-speed quantum cryptography.
• Generalizability: While focused on NV centers, the experimental and theoretical results extend to other solid-state single-photon sources and defect centers in diamond, broadening the applicability of the findings.
• Efficiency: The study proves that using multiple emitters (which introduces multi-photon events) does not degrade the randomness quality below usable thresholds, allowing for a trade-off between speed and purity that favors high-speed applications.

In conclusion, this work establishes the time-of-arrival scheme using NV centers as a superior alternative to branching-path schemes for solid-state QRNGs, offering a balance of high speed, simplicity, and high-quality randomness suitable for next-generation cryptographic applications.