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arxiv: 2604.26554 · v1 · submitted 2026-04-29 · 🪐 quant-ph

Random Number Generators in Advanced Optical Experiments: A Comparative Analysis of Semiclassical, Quantum, and Hybrid Architectures

Daniil D. Reshetnikov , Anna A. Kretova , Anastasia A. Fominova , Evgenii A. Vashukevich , Tatiana Y. Golubeva , Kirill S. Tikhonov This is my paper

Pith reviewed 2026-05-07 10:38 UTC · model grok-4.3

classification 🪐 quant-ph
keywords random number sequencesoptical random number generationhybrid architectureheralded single-photon sourceattenuated laserrandomness extractorsquantum optics
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The pith

A hybrid architecture mixing attenuated laser and single-photon light generates raw random sequences that can surpass those refined by randomness extractors.

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

The paper evaluates optical architectures for random number generation, weighing the high speed of attenuated lasers against the better randomness of slower heralded single-photon sources. It introduces a hybrid design that mixes light from both to combine their strengths. Key finding is that unprocessed sequences from this hybrid can match or beat the randomness quality of sequences run through powerful extractors. This is relevant because many applications require fast, high-quality random numbers integrable directly into optical experiments.

Core claim

By mixing radiation from an attenuated laser and a heralded single-photon source, the hybrid architecture generates random number sequences at enhanced rates while maintaining or improving statistical quality, such that the unprocessed sequences sometimes outperform those subjected to randomness extractors.

What carries the argument

The hybrid architecture that combines mixed radiation from an attenuated laser as a quasi-single-photon source and a heralded single-photon source to balance generation rate with entropy.

Load-bearing premise

The mixed radiation from the attenuated laser and heralded single-photon sources maintains statistical independence and high entropy without introducing unforeseen correlations or biases from the combination process.

What would settle it

An experiment that measures unexpected correlations or entropy loss in the hybrid raw output, making its randomness fall below that of extracted sequences from the individual sources, would disprove the claim.

Figures

Figures reproduced from arXiv: 2604.26554 by Anastasia A. Fominova, Anna A. Kretova, Daniil D. Reshetnikov, Evgenii A. Vashukevich, Kirill S. Tikhonov, Tatiana Y. Golubeva.

Figure 1
Figure 1. Figure 1: The coherent quasi-single-photon source of view at source ↗
Figure 2
Figure 2. Figure 2: The heralded (genuine) single-photon source view at source ↗
Figure 3
Figure 3. Figure 3: The hybrid source of RNSs: the χ 2 -crystal gen￾erates the Bell state |ψ +⟩ = 2−1/2 (|H1V2⟩ + |V1H2⟩), representing a pair of photons in a superposition of hor￾izontal (H) and vertical (V) polarizations. One photon from the pair is reflected and strikes the detector 3 (D3). Simultaneously, the entire output of the coherent source (CS) is reflected by the same PBS and mixed with the heralded photons. After … view at source ↗
Figure 4
Figure 4. Figure 4: Median p-values of the NIST Statistical Test Suite for the five RNSs sources: a) Coherent single view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of p-value distributions obtained for raw and post-processed sequences for: a) Coherent single view at source ↗
Figure 6
Figure 6. Figure 6: The percentage of tests passed by the subse view at source ↗
Figure 7
Figure 7. Figure 7: Randomness quality as a function of mixing frequency for: view at source ↗
Figure 8
Figure 8. Figure 8: a) Median p-values from the NIST Statistical Test Suite for randomness quality assessment. Results are view at source ↗
Figure 9
Figure 9. Figure 9: The example of the stream numbering proposed by V.F. Babkin. a) Step 1: a Bernoulli sequence view at source ↗
Figure 10
Figure 10. Figure 10: The distribution of photocount events for view at source ↗
Figure 11
Figure 11. Figure 11: The dependence of the coincident count rates 1 view at source ↗
Figure 12
Figure 12. Figure 12: Randomness quality as a function of mixing frequency for: view at source ↗
read the original abstract

Random numbers sequences (RNSs) play a vital role in various scientific and engineering applications. They are critical to the integrity of classical and quantum cryptography, the accuracy of mathematical modeling and Monte Carlo simulations, and the core mechanics of applications in fields as diverse as gambling and statistical sampling. While the primary criteria for RNSs sources are their quality and generation rate, their integration into experimental designs is equally significant for many fundamental physical tests and applications. This work presents a comparative analysis of optical random number generation architectures, which can be seamlessly included into various advanced classical and quantum optical experimental schemes. In particular, we evaluate the trade-off between the high generation rate of an attenuated laser (a quasi-single-photon source) and the superior statistical quality of a heralded single-photon source operating at a much lower frequency. To overcome the limitations of each individual source, we propose and examine a novel hybrid architecture that utilizes their mixed radiation, enabling the generation of highquality RNSs at an enhanced rate. Furthermore, we demonstrate that the raw sequences generated by such a source can not only exhibit but, in some cases, even surpass the degree of randomness achieved by sequences processed through powerful randomness extractors.

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

2 major / 1 minor

Summary. The manuscript conducts a comparative analysis of semiclassical (attenuated laser), quantum (heralded single-photon), and hybrid optical random number generator architectures for use in advanced experiments. It highlights the trade-off between generation rate and statistical quality, introduces a hybrid source combining both, and claims that raw output from the hybrid can, in some cases, exceed the randomness quality of extractor-processed sequences from the individual sources.

Significance. Should the empirical claims be verified, this could offer a valuable practical advancement in random number generation for optical setups, allowing higher rates with maintained or improved quality without extractor overhead. It addresses a real need in integrating RNG into quantum and classical optical experiments. The work would benefit from explicit comparisons to existing methods in the literature.

major comments (2)
  1. Abstract: The assertion that 'the raw sequences generated by such a source can not only exhibit but, in some cases, even surpass the degree of randomness achieved by sequences processed through powerful randomness extractors' is not accompanied by any quantitative data, specific randomness metrics (such as min-entropy estimates or test suite results), error bars, or statistical analysis, rendering the claim unverifiable from the provided text.
  2. Hybrid architecture description: The hybrid architecture's ability to maintain or increase min-entropy without introducing correlations from the mixing process is central to the claim of surpassing extractors, yet no analytic derivation, covariance matrix analysis, or empirical cross-correlation measurements are presented to support the independence assumption.
minor comments (1)
  1. Abstract: The abstract refers to 'evaluation and demonstration' but does not outline the specific experimental setup, number of samples, or randomness testing procedures used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding verifiability and supporting analysis. We address each major comment below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: Abstract: The assertion that 'the raw sequences generated by such a source can not only exhibit but, in some cases, even surpass the degree of randomness achieved by sequences processed through powerful randomness extractors' is not accompanied by any quantitative data, specific randomness metrics (such as min-entropy estimates or test suite results), error bars, or statistical analysis, rendering the claim unverifiable from the provided text.

    Authors: We agree that the abstract, as currently written, does not contain the quantitative details needed to make the claim immediately verifiable. The body of the manuscript (Sections 3 and 4) presents the supporting min-entropy estimates, NIST test-suite results, and statistical comparisons, but these are not summarized in the abstract. In the revised version we will shorten the abstract slightly and insert the key quantitative metrics (average min-entropy per bit for each architecture, representative p-value ranges, and error-bar information) so that the claim is self-contained and directly supported by data. revision: yes

  2. Referee: Hybrid architecture description: The hybrid architecture's ability to maintain or increase min-entropy without introducing correlations from the mixing process is central to the claim of surpassing extractors, yet no analytic derivation, covariance matrix analysis, or empirical cross-correlation measurements are presented to support the independence assumption.

    Authors: The referee is correct that the manuscript does not presently contain an analytic derivation, an explicit covariance-matrix treatment, or tabulated cross-correlation measurements. The current text relies on the physical separation of the two sources and the low mean photon number to argue for statistical independence. We will add the requested material in a new subsection: (i) a short analytic argument based on the independent Poissonian statistics of the attenuated laser and the heralded single-photon detections, (ii) the measured cross-correlation function between the two input streams, and (iii) the covariance matrix of the resulting bit sequences, all with appropriate error bars. These additions will directly substantiate the independence assumption underlying the min-entropy claim. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparison without derivations or self-referential reductions

full rationale

The manuscript is a comparative experimental analysis of optical RNG sources (attenuated laser, heralded single-photon, and their hybrid mix) with the central claim that raw hybrid sequences can match or exceed post-extractor randomness. No equations, parameter fits, uniqueness theorems, or derivation steps appear in the provided text. The hybrid independence assumption is an unverified modeling premise rather than a self-definitional loop or a fitted quantity renamed as a prediction. No self-citations are invoked to justify load-bearing steps, and the result is presented as a demonstration rather than a closed mathematical reduction to its own inputs. The paper is therefore self-contained against external benchmarks with no detectable circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the hybrid concept implicitly assumes statistical properties of mixed radiation without detailing supporting assumptions.

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