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arxiv: 2504.18795 · v1 · submitted 2025-04-26 · 🪐 quant-ph

Highly integrated broadband entropy source for quantum random number generators based on vacuum fluctuations

Xuyang Wang , Yuqi Shi , Ning Wang , Jie Yun , Jiaxu Li , Yanxiang Jia , Shuaishuai Liu , Zhenguo Lu
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Jun Zou Yongmin Li
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Pith reviewed 2026-05-22 18:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum random number generatorvacuum fluctuationsentropy sourcesilicon photonicsbalanced homodyne detectorequalizer technologyrandom number generation rate
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The pith

A compact hybrid chip generates quantum random numbers at 67.9 Gbps from vacuum fluctuations after equalization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents a highly integrated broadband entropy source for quantum random number generators that relies on vacuum fluctuations captured by a balanced homodyne detector. The core component is a small hybrid chip combining a laser with silicon photonics that measures only 6.3 by 2.6 by 1.5 cubic millimeters. The detector achieves a 2.4 GHz bandwidth and a quantum-to-classical noise ratio of 9.51 dB. Equalizer technology removes dependence between adjacent samples to deliver generation rates of 67.9 Gbps on average and 61.9 Gbps in the worst case. A sympathetic reader would care because this level of integration and speed could make quantum-secure random number generation more feasible for real-world cryptographic systems.

Core claim

The authors designed and experimentally verified a highly integrated broadband entropy source for a quantum random number generator based on vacuum fluctuations. The core is a hybrid laser-and-silicon-photonics chip of size 6.3 × 2.6 × 1.5 mm³. A balanced homodyne detector using cascaded radio-frequency amplifiers reaches a 3 dB bandwidth of 2.4 GHz and common-mode rejection above 25 dB. The quantum-to-classical-noise ratio is 9.51 dB at 1 mA photoelectron current. After equalizer optimization that eliminates dependence of adjacent samples, the quantum random number generation rate reaches 67.9 Gbps under average conditional minimum entropy and 61.9 Gbps under worst-case conditional minimum

What carries the argument

The hybrid laser-and-silicon-photonics chip with its cascaded-amplifier balanced homodyne detector that measures broadband vacuum fluctuations while suppressing classical noise.

If this is right

  • The small chip size allows vacuum-fluctuation QRNG entropy sources to fit into compact integrated systems.
  • Equalizer processing removes sample dependence and thereby supports generation rates above 60 Gbps.
  • The reported 2.4 GHz bandwidth and 25 dB common-mode rejection establish a practical noise floor for high-speed operation.
  • The device advances integrability of vacuum-based QRNGs without requiring larger discrete components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the integration scales, such chips could enable mass production of high-speed QRNG modules for consumer devices.
  • Higher bandwidth versions might extend the approach to even faster rates needed for future quantum communication links.
  • Real-world deployment tests could check whether the negligible classical noise assumption holds under varying temperatures or electromagnetic conditions.

Load-bearing premise

The measured noise after the balanced homodyne detector and equalizer remains dominated by vacuum fluctuations with negligible residual classical correlations or bias from the optimization.

What would settle it

A measured quantum-to-classical-noise ratio falling well below 9.51 dB or the appearance of measurable correlations in the equalized output samples would show the claimed rates cannot be sustained.

Figures

Figures reproduced from arXiv: 2504.18795 by Jiaxu Li, Jie Yun, Jun Zou, Ning Wang, Shuaishuai Liu, Xuyang Wang, Yanxiang Jia, Yongmin Li, Yuqi Shi, Zhenguo Lu.

Figure 2
Figure 2. Figure 2: FIG. 2. Structure of our QRNG based on vacuum fluctuations. GC: [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. 3 dB bandwidth of the existing integrated entropy sources [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Integration of the laser and SiPh chips: (a) Mount A, (b) [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Circuit diagram and the layout of cascaded RFAs circuits. (a) Circuit diagram. (b) The structure of the high-frequency transmission [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Noise power spectrum of the integrated BHD. The resolution [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Average conditional minimum entropy and worst-case con [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Equalization, correlation, and probability distribution of the data, and the randomness test results. Noise power spectra when the [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
read the original abstract

In this work, we designed and experimentally verified a highly integrated broadband entropy source for a quantum random number generator (QRNG) based on vacuum fluctuations. The core of the entropy source is a hybrid laser-and-silicon-photonics chip, which is only 6.3 $ \times $ 2.6 $ \times $ 1.5 mm$^{3}$ in size. A balanced homodyne detector based on cascaded radio-frequency amplifiers in the entropy source achieves a 3 dB bandwidth of 2.4 GHz and a common-mode rejection ratio above 25 dB. The quantum-to-classical-noise ratio is 9.51 dB at a photoelectron current of 1 mA. The noise equivalent power and equivalent transimpedance are 8.85$\,\text{pW}/\sqrt{\text{Hz}}$ , and 22.8 k$\Omega$, respectively. After optimization using equalizer technology that eliminates the dependence of adjacent samples, the quantum random number generation rate reaches 67.9 Gbps under average conditional minimum entropy and 61.9 Gbps under the worst-case conditional minimum entropy. The developed hybrid chip enhances the integrability and speed of QRNG entropy sources based on vacuum fluctuations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents the design and experimental verification of a compact hybrid laser-silicon photonics chip (6.3 × 2.6 × 1.5 mm³) serving as a broadband entropy source for vacuum-fluctuation QRNGs. It reports a balanced homodyne detector with 2.4 GHz 3 dB bandwidth, >25 dB common-mode rejection ratio, 9.51 dB quantum-to-classical noise ratio at 1 mA photocurrent, and, after equalizer optimization to remove adjacent-sample correlations, QRNG rates of 67.9 Gbps (average conditional minimum entropy) and 61.9 Gbps (worst-case conditional minimum entropy).

Significance. If the post-equalizer noise remains vacuum-fluctuation dominated with negligible residual classical correlations or optimization-induced bias, the work would advance integrated, high-speed QRNG entropy sources by combining high bandwidth, good CMRR, and competitive extraction rates in a small footprint. The experimental integration and concrete performance numbers are strengths, though the rates hinge on the validity of the min-entropy estimates.

major comments (1)
  1. Equalizer optimization and entropy calculation: The central performance claims (67.9 Gbps average and 61.9 Gbps worst-case) rely on the assertion that equalization fully eliminates adjacent-sample dependence while preserving the vacuum-fluctuation statistics. With a reported QNR of only 9.51 dB at 1 mA (implying classical noise remains ~10 % of total power), the manuscript should supply post-equalizer autocorrelation functions, higher-order statistics, or an explicit adversary model to bound any residual classical leakage or filter-induced bias in the conditional min-entropy; without these, the rates cannot be fully substantiated.
minor comments (2)
  1. The noise-equivalent power (8.85 pW/√Hz) and equivalent transimpedance (22.8 kΩ) are reported without explicit reference to the measurement conditions or frequency range over which they were extracted.
  2. Clarify whether the quoted chip dimensions include the laser or only the silicon-photonics portion, and whether the balanced detector is monolithically integrated or hybrid-assembled.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the single major comment below and have revised the manuscript to include additional supporting data and clarifications on the entropy estimation procedure.

read point-by-point responses

  1. Referee: Equalizer optimization and entropy calculation: The central performance claims (67.9 Gbps average and 61.9 Gbps worst-case) rely on the assertion that equalization fully eliminates adjacent-sample dependence while preserving the vacuum-fluctuation statistics. With a reported QNR of only 9.51 dB at 1 mA (implying classical noise remains ~10 % of total power), the manuscript should supply post-equalizer autocorrelation functions, higher-order statistics, or an explicit adversary model to bound any residual classical leakage or filter-induced bias in the conditional min-entropy; without these, the rates cannot be fully substantiated.

    Authors: We agree that additional evidence strengthens the central claims. In the revised manuscript we now include the post-equalizer autocorrelation functions computed over 100 lags, which fall to the level of statistical fluctuations, together with the skewness and kurtosis of the equalized samples to confirm consistency with a Gaussian distribution. The conditional minimum-entropy extraction already incorporates the measured 9.51 dB QNR, so the ~10 % classical-noise power is explicitly accounted for in both the average and worst-case bounds. Because the equalizer is a deterministic linear filter applied uniformly to the digitized trace, it does not introduce sample-dependent bias beyond the noise ratio already used in the entropy calculation. We have added a short paragraph discussing these points and the assumptions underlying the min-entropy estimates. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental QRNG rates derived from direct hardware measurements

full rationale

The paper reports the design, fabrication, and experimental characterization of a hybrid integrated entropy source for vacuum-fluctuation QRNG. All load-bearing claims—the 9.51 dB QNR, 2.4 GHz bandwidth, and final 67.9 Gbps / 61.9 Gbps rates—are obtained from measured spectra, autocorrelation functions, and conditional min-entropy estimates performed on the physical output of the balanced homodyne detector plus equalizer. These quantities are computed from raw time-series data rather than from any self-referential definition, fitted parameter that is then renamed as a prediction, or uniqueness theorem imported via self-citation. The equalizer step is presented as a standard whitening filter whose performance is validated by post-processing statistics; no equation reduces to its own input by construction. The work is therefore self-contained against external benchmarks and receives a score of zero.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an experimental hardware demonstration relying on standard quantum optics assumptions rather than new theoretical constructs or fitted parameters.

axioms (1)
  • domain assumption Vacuum fluctuations provide a source of true quantum entropy suitable for random number generation when properly detected and processed.
    This underpins the entire entropy source design and is invoked in the description of the balanced homodyne detector approach.

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Forward citations

Cited by 1 Pith paper

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