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REVIEW 4 major objections 7 minor 92 references

Quantum Random Number Generator (QRNG): Theoretical and Experimental Investigations

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A home-built balanced homodyne detector extracts 5 bits of quantum vacuum noise from each 8-bit sample, and the post-processed stream passes all 15 tests of one statistical suite and all 31 tests of another, at about 50 Mbps.

desk verdict A workmanlike vacuum-noise QRNG lab report whose central claim—certified 5-bit quantum entropy per sample—is unsupported because the LFSR post-processing cannot do what the paper says and the entropy estimate does not separate quantum from classical noise. read the letter →

arxiv 2506.02441 v1 pith:I4MPZKDF submitted 2025-06-03 quant-ph

Zeshan Haider , Muhammad Haroon Saeed , Muhammad Ehsan-ul-Haq Zaheer , Zeeshan Ahmed Alvi , Muhammad Ilyas , Tahira Nasreen , Muhammad Imran , Rameez Ul Islam
show 1 more author
Manzoor Ikram
This is my paper · ORCID
classification quant-ph
keywords quantumrandomnumbergenerationvacuumfluctuationsbalancedhomodynedetectionmin-entropyLFSRextractorstatisticalrandomnesstestsshot-noiselimitautocorrelation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports a tabletop quantum random number generator that draws randomness from the quantum vacuum: an 852 nm local oscillator, a polarizing beam splitter whose unused port admits the vacuum, and a home-built 10 MHz balanced homodyne detector convert the vacuum's amplitude-quadrature fluctuations into a measurable current. Sampling that current at 8 bits per point, the authors estimate a worst-case min-entropy of 5 bits per sample, attribute that entropy to quantum vacuum noise, and then pass the extracted bit stream through a 63-bit linear feedback shift register used as an extractor. They report that the final stream passes all 15 tests of one standard statistical suite and all 31 tests of another battery, that autocorrelation drops to a few thousandths after one bit, that the file resists compression, and that the generation speed is about 50 Mbps. If true, the result matters because it offers a relatively simple QRNG that avoids single-photon detectors, interferometric delay lines, and complex calibration.

What carries the argument

The balanced homodyne detector is the physical engine: two matched photodiodes receive the two outputs of a 50:50 beam splitter, their photocurrents are subtracted, and the difference is directly proportional to the vacuum amplitude quadrature, so the local oscillator amplifies vacuum-scale fluctuations above electronic noise. The post-processing chain is the statistical engine: 8-bit sampling, a min-entropy estimate of 5 bits per sample, retention of the 5 most significant bits, and application of a 63-bit linear feedback shift register (a shift register whose new bit is a linear function of previous bits) in serial as the claimed extractor.

What would settle it

With the local oscillator switched off, record the electronic noise alone and push it through the identical 8-bit sampling, 5-most-significant-bit selection, and 63-bit LFSR post-processing. If the LO-off stream has a per-sample min-entropy comparable to 5 bits and passes the same 15-plus-31 statistical tests, then the reported tests and entropy estimate do not distinguish quantum vacuum noise from classical electronic noise, and the central claim fails.

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Extended reading notes

Core claim

The central discovery is that the homodyne difference current, $\Delta i = S\hbar\omega\tau (2\bar{\alpha}_{\mathrm{lo}})\delta X_{1,\mathrm{vac}}$, isolates the vacuum quadrature $\delta X_{1,\mathrm{vac}}$ on top of a fixed classical electronic background; the variance of the total noise grows with local-oscillator power until it saturates at about 10 mW, which the paper takes as the shot-noise limit. At that operating point the raw 8-bit samples have a Gaussian profile whose worst-case min-entropy is about 5 bits per 8-bit sample, so the authors treat 5 bits of each sample as the quantum contribution and discard the remaining 3 bits. Keeping the 5 most significant bits and applying a 63-bit LFSR in serial is claimed to flatten the Gaussian profile into an equiprobable distribution; the extracted stream then passes all 15 tests of the standard statistical suite and all 31 tests of the second battery on a 50 GB file, with autocorrelation reduced to a few thousandths after lag one. The paper's conclusion is that a certified, environment-robust QRNG with about 50 Mbps output can be built from these components, with a plausible upgrade path to 500 Mbps.

Load-bearing premise

The load-bearing assumption is that a serial 63-bit LFSR, a linear bit operation, actually flattens the Gaussian raw-noise distribution into a uniform one and so acts as a randomness extractor; since a linear map cannot increase entropy, if that flattening is not a genuine extraction, the test passes certify only the LFSR's own pseudorandom behavior, not quantum vacuum randomness.

Editorial extensions

If this is right

  • A QRNG for cryptographic and simulation use can be assembled from a laser, a half-wave plate, a polarizing beam splitter, two photodiodes, and a 10 MHz difference circuit, with no single-photon detectors.
  • The 5-bit-per-8-bit-sample min-entropy estimate provides a conservative entropy budget: three bits per sample can be discarded in post-processing while preserving quantum randomness.
  • Operating at the 10 mW shot-noise-limit point maximizes the quantum contribution to the total noise variance, giving a simple calibration rule for similar setups.
  • The reported pass on all 15-plus-31 statistical tests means the output is statistically indistinguishable from ideal random bits on the tested file size, which is what applications require.
  • Raising the ADC sampling rate and replacing USB with PCI data transfer is claimed to raise output to about 500 Mbps, with stronger hashing needed once faster sampling adds more bias.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because an LFSR is a linear reversible map, it cannot add entropy; the certified-randomness claim therefore rests on the 5-bit min-entropy measured before extraction, and a stronger certification would use a keyed universal hash rather than an LFSR.
  • Editorial inference: the same post-processing would plausibly make any stationary Gaussian electronic noise look random to the same test batteries; a decisive check is to run the full 8-bit-to-LFSR pipeline on the local-oscillator-off data and show that its per-sample min-entropy falls well below 5 bits.
  • Editorial inference: if the entropy estimate is correct, the device's 50 Mbps rate is an estimate of certified quantum randomness; the unextracted raw output, with its Gaussian bias and temporal correlations, should not be used directly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 7 minor

Summary. The paper reviews quantum random number generator approaches and presents an experimental vacuum-fluctuation QRNG based on balanced homodyne detection. It reports an SP800-90B min-entropy estimate of about 5 bits per 8-bit sample, attributes this entropy to quantum vacuum noise, applies a 63-bit LFSR as a 'potential extractor' after discarding 3 bits, and claims that the extracted stream passes the NIST, Dieharder, compression, and autocorrelation tests, yielding a certified quantum random bit rate of about 50 Mbps.

Significance. If the central claims were supported, the paper would offer a simple and accessible vacuum-fluctuation QRNG with a clear entropy assessment. The authors provide a broad literature overview, an indigenous balanced homodyne detector, and a systematic battery of statistical tests. However, the load-bearing steps—the LFSR extractor and the attribution of all estimated min-entropy to quantum noise—are not justified; the statistical tests cannot certify quantum origin. The paper's value as a standalone research contribution is therefore limited, though it may be useful as a tutorial-style account of building and testing a homodyne-based QRNG.

major comments (4)
  1. [Section V, Fig. 7] The manuscript states that 'the biased profile of quantum noise (Gaussian) is flattened by using LFSR as a potential extractor algorithm' and that the extracted counts are 'equally probable in all bins.' A 63-bit LFSR is a deterministic linear map over GF(2); it cannot increase entropy, cannot transform a Gaussian-shaped source distribution into a uniform one, and cannot generate fresh randomness. No seed, tap polynomial, output mapping, or leftover-hash argument is provided. Consequently, the uniformity of the processed stream and the passing of NIST and Dieharder tests do not certify the quantum origin or the unpredictability of the bits; at best they show that the post-processed stream resembles a pseudo-random sequence.
  2. [Section V.A] The SP800-90B min-entropy estimate of about 5 bits per 8-bit sample is applied to the full raw ADC output, which comprises vacuum noise, electronic noise, and environmental noise. The paper offers no model that separates the quantum component from the classical components (e.g., a shot-noise calibration or a conditional-entropy calculation), so the statement that 'the contribution of quantum noise is 5 bits' (Section V) is unsupported. The same estimate is used both to set the extraction rate (discarding 3 bits) and to assert the quantum nature of the source, which renders the attribution circular.
  3. [Section V, Fig. 9] The claim that 10 mW is the 'shot-noise limit' is not established. The variance-versus-power data are shown on a log plot, but the paper does not provide a quantitative fit to σ²_total = σ²_c + σ²_q, nor a comparison with the expected shot-noise scaling, nor a verification that the excess variance is free of classical intensity noise. The description of the electronic-noise measurement with the LO switched off is qualitative; a quantitative control experiment is required to support the claim that the added variance is quantum-limited.
  4. [Section V.B and Conclusion] The claimed output rate of about 50 Mbps is not derivable from the stated parameters: 10 MSa/s × 8 bits/sample = 80 Mbps raw, and after discarding 3 bits and applying the LFSR the output rate depends on the exact post-processing mapping, which is not specified. The paper should state the number of output bits per input sample and the throughput of the LFSR stage, and it should clarify whether the 50 Mbps figure is measured or inferred.
minor comments (7)
  1. [Section I.A] The phrase 'chona's circuit' should read 'Chua's circuit'.
  2. [Section IV] The phrase 'Continues Wave' should read 'Continuous Wave'.
  3. [Conclusion] The phrase 'Teoplitz function' should read 'Toeplitz function'.
  4. [Section VII] The data availability statement says all data are presented graphically and therefore no data are associated, which contradicts the claimed 100 Mb NIST file and 50 GB Dieharder file; raw data or a link should be provided for reproducibility.
  5. [Section V.A] The sentence 'The min-entropy estimator is based on the assumption that the probability distribution of the i.i.d. random variables is uniform' is incorrect; SP800-90B min-entropy estimators do not assume uniformity, and the following two sentences conflate the estimator with a uniformity assumption.
  6. [References] Reference [39] (multiphoton blockade) is not relevant to the claim about super-Poissonian scattering; please replace or remove it.
  7. [Figures 9, 12, and 13] The captions of Figures 9, 12, and 13 do not fully specify the meaning of all curves, dots, and bars; each caption should identify every plotted quantity and the significance threshold used.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed quantum contribution of 5 bits is the fitted min-entropy estimate from the same raw data, then reused to set the extraction rate.

  1. fitted input called prediction [Section V, Experimental Investigations, Results and Discussion, paragraphs following Fig. 7 and before Fig. 10]
    "The value of Hmin comes out to be about 5, predicting that out of 8 bit sample, the contribution of quantum noise is 5 bits. ... we have discarded 3 bits per sample (of 8 bits) as the contribution of quantum noise is 5 bits per sample suggested by min-entropy value i.e., Hmin = 5bits. Keeping the 5 MSB bits and applying the LFSR in serial we obtain the extracted data."

    The 'contribution of quantum noise' is not independently measured; it is set equal to the SP800-90B min-entropy estimate computed from the raw ADC samples, which include electronic, environmental and classical noise with no quantum-conditioning control at this stage. That same fitted Hmin value is then used to decide that exactly 5 of the 8 raw bits are quantum, to discard the remaining 3 bits, and to define the extracted stream. Thus the predicted quantity (5 quantum bits per sample) is by construction identical to the fitted entropy estimate, and the subsequent randomness certification applies to a stream whose length and content were chosen using that same estimate.

full rationale

The paper contains no load-bearing self-citation: references [39] and [40] include overlapping authors but are cited only for general background and are not used to justify the central randomness claim. The main circularity is the entropy attribution. The 5-bit-per-sample 'quantum contribution' is presented as a prediction, but the paper's own text shows it is simply the SP800-90B min-entropy estimate of the raw data. This same estimate is then used to set the post-processing extraction rate (keep 5 MSB, discard 3 bits), after which the LFSR output is declared maximally unpredictable and certified by NIST and Dieharder. Since the extracted stream is deterministically derived from the same samples whose entropy estimate was used to choose the extraction parameters, the claimed 5-bit quantum entropy reduces to the fitted input by construction. There is independent physical content in the variance-versus-LO-power measurement and the homodyne equation, so the circularity is partial rather than total. The LFSR's inability to add entropy is a correctness concern, not a circularity concern, and is not scored here.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim relies on several standard quantum-optics assumptions, two ad hoc assumptions specific to this paper (the attribution of the full entropy estimate to quantum noise, and the LFSR as a uniformizing extractor), and three fitted or estimated parameters (LO power, entropy cutoff, LFSR length). No new physical entities are introduced.

free parameters (3)
  • LO operating power = 10 mW
    Selected from the variance-versus-power measurements (Figs. 8 and 9) as the point where total and quantum variance curves coincide; used as the shot-noise-limit operating point.
  • Min-entropy cutoff = 5 bits per 8-bit sample
    Obtained from NIST SP800-90B on the raw data and then used to keep 5 MSBs per sample; this is an estimate, not a first-principles value.
  • LFSR length = 63 bits
    Chosen without stated justification for the serial extractor.
assumptions (5)
  • standard math Balanced homodyne detection measures the amplitude quadrature of the vacuum field with the LO providing gain.
    Relied on in Section IV, Eq. (7) and Fig. 6.
  • domain assumption The total noise variance is the sum of classical and quantum variances, with classical noise independent of LO power.
    Used in Section V in the variance decomposition sigma_total^2 = sigma_c^2 + sigma_q^2.
  • domain assumption The quantum vacuum fluctuations produce Gaussian-distributed photocurrent differences.
    Assumed when fitting Gaussian histograms in Fig. 7 and when extracting bits.
  • ad hoc to paper The SP800-90B min-entropy estimate of the full raw noise can be attributed to quantum vacuum fluctuations.
    Introduced in Section V to support the claim of 5 bits of quantum entropy per sample; no model separates classical and quantum contributions.
  • ad hoc to paper A 63-bit LFSR applied in serial acts as a randomness extractor that flattens the Gaussian distribution into a uniform one.
    Stated in Sections IV and V; this is a linear operation and cannot by itself make the output distribution uniform, so the premise is suspect.

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Cite this review

Pith. "Pith review of Quantum Random Number Generator (QRNG): Theoretical and Experimental Investigations." pith.science (2026). https://pith.science/paper/I4MPZKDF

@misc{pith2026250602441,
  author       = {Pith},
  title        = {Pith review of: Quantum Random Number Generator (QRNG): Theoretical and Experimental Investigations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I4MPZKDF}},
  note         = {Machine review of arXiv:2506.02441}
}
read the original abstract

Quantum Random Number Generators (QRNGs) emerged as a promising solution for generating truly random numbers. In the present article, we give an overview of QRNGs highlighting the merits and demerits of various strategies briefly. Then opting for the best-case scenario, we present the in-depth experimental explorations for building and characterizing QRNG using the homodyne detection technique to measure the quadrature amplitude of quantum vacuum fluctuations. Since entropy assessment plays a fundamental role in authenticating the true randomness, a comprehensive description of entropy and how it evaluates the quality of randomness of the source is illustrated. Our experimental setup, apart from the hardware, includes a diverse set of testing techniques including NIST statistical/entropy suites, Dieharder tests battery, and autocorrelation coefficient to verify the randomness and statistical properties of the generated random numbers. We believe that our experimental investigations provide a valuable resource for building QRNGs for a wide range of applications.

Figures

Figures reproduced from arXiv: 2506.02441 by the authors.

Figure 1
Figure 1. FIG. 1. QRNG based on single photons and a 50:50 Beam [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The schematic diagram for QRNG based on photon [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. The illustrative diagram for the engineering schemat [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Experimental Schematics for QRNG based on Quan [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic diagram of Balanced Homodyne Detector [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (left)Typical 1 million raw data collected under op [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The logarithmic plot of variance of signal amplitude [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Autocorrelation coefficient calculation of raw [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Typical results of standard NIST Statistical Test [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of original and compressed sizes of [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Dieharder test results for a sequence of obtained [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]

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