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arxiv: 2605.04162 · v1 · submitted 2026-05-05 · 🪐 quant-ph

Recognition: 3 theorem links

· Lean Theorem

Boson Sampling with a reconfigurable 128 modes 3D integrated photonic circuit

Alessandro Ciorra, Andrea Crespi, Daniel Carvalho de Salles, Fabio Sciarrino, Francesco Ceccarelli, Francesco Hoch, Gonzalo Carvacho, Marco Gardina, Nicol\`o Spagnolo, Niki Di Giano, Roberto Osellame, Simone Di Micco, Taira Giordani

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:50 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Boson samplingintegrated photonicsreconfigurable circuitssingle-photon sourcesquantum random number generation3D photonic integrationquantum optics
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The pith

A 128-mode reconfigurable 3D photonic chip performs Boson Sampling with up to four photons and produces verifiable random numbers.

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

The paper presents a new integrated 3D photonic circuit with 128 modes that can be reprogrammed on the fly using thermo-optic shifters to apply different transformations to single photons. The authors ran Boson Sampling experiments on this chip with one to four photons taken from a quantum-dot source and compared the measured output patterns to ideal theoretical predictions. The close agreement confirms both that the device implements the intended operations and that the sampling process can generate random numbers. A sympathetic reader would care because Boson Sampling is a leading candidate for demonstrating quantum advantage, and a stable, scalable hardware platform is required to move from proof-of-concept to useful applications. The work shows that 3D integration and active control can reach the mode counts needed for such tasks.

Core claim

We introduce an integrated, reconfigurable 3D photonic device with 128 modes for manipulation of single-photon quantum states (Qolossus 3D). Leveraging a continuously coupled architecture and thermo-optic programmability, the platform implements reconfigurable unitary transformations at unprecedented scale for integrated quantum optics. Exploiting indistinguishable single photons demultiplexed from a quantum dot source, we perform Boson Sampling across the large-dimensional chip and analyse the resulting output distributions for up to 4 photons. We then exploit it to demonstrate randomness generation via Boson Sampling. Agreement with theoretical predictions validates both the device's re

What carries the argument

The 128-mode reconfigurable 3D integrated photonic circuit (Qolossus 3D) that uses a continuously coupled waveguide architecture and thermo-optic phase shifters to realize programmable unitary transformations on photon states.

If this is right

  • The device can execute reconfigurable unitary transformations on single-photon states at a scale of 128 modes.
  • Boson Sampling output distributions for up to four photons agree with theoretical predictions.
  • The same platform can generate random numbers whose unpredictability follows from the hardness of Boson Sampling.
  • The 3D integration and active control demonstrate stability and precise phase control suitable for further quantum information tasks.

Where Pith is reading between the lines

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

  • The reconfigurability demonstrated here could allow the same chip to be reused for other linear-optical protocols beyond standard Boson Sampling.
  • If the mode count and photon number can be increased while preserving indistinguishability, the platform would move closer to regimes where classical simulation becomes intractable.
  • The 3D architecture may offer lower loss and crosstalk than planar equivalents, enabling even larger mode counts in future devices.

Load-bearing premise

The input photons remain sufficiently indistinguishable and the thermo-optic phase shifters realize the programmed unitary transformations with errors small enough that the observed output distributions still match the ideal Boson Sampling predictions.

What would settle it

If the measured output probability distributions for three- or four-photon inputs deviate from the theoretical Boson Sampling probabilities by more than the reported experimental uncertainty, the claim of successful large-scale reconfigurable operation would be falsified.

Figures

Figures reproduced from arXiv: 2605.04162 by Alessandro Ciorra, Andrea Crespi, Daniel Carvalho de Salles, Fabio Sciarrino, Francesco Ceccarelli, Francesco Hoch, Gonzalo Carvacho, Marco Gardina, Nicol\`o Spagnolo, Niki Di Giano, Roberto Osellame, Simone Di Micco, Taira Giordani.

Figure 1
Figure 1. Figure 1: High-dimensional Boson Samplers within a 3D photonic chip. a) Boson Sampling exploits multi-photon interference in a randomly extracted large-scale optical transformation to perform a task that is computationally intractable for classical systems. The programmable high-dimensional integrated optical circuit is realised through the femtosecond laser writing technique and comprises 128 optical modes arranged… view at source ↗
Figure 2
Figure 2. Figure 2: Experimental setup Qolossus 3D. a) On-demand photon generation. We employ a Quantum Dot (QD) single-photon source housed in a cryostation maintained at 4 K, operated under resonant excitation. The emitted stream of single photons is directed to a time-to-space acousto-optic demultiplexing system, which routes the photons into four separate spatial paths. Temporal synchronisation across these paths is achie… view at source ↗
Figure 3
Figure 3. Figure 3: Reconfigurability of the 3D integrated device and Haar-random sampling. a) Squared moduli distribution of the matrix elements Uij (P) when varying the currents applied to different numbers of heaters (from 2 up to 17). The experimental data are obtained by injecting single photons in a given input mode and recording the output photon distributions. The expected histogram corresponds to the numerical simula… view at source ↗
Figure 4
Figure 4. Figure 4: Validation of Boson Sampling data. Sequential likelihood–ratio tests on three-fold and four-fold, collision-free events collected at the output of the 128-mode device. In (a) and (b), examples of the one-photon and two-photon distributions used for the reconstruction of the unitary matrix. Panel (a) highlights in white the 20 output ports that were not measured in the experiment. (c) (e) Counter Wk for the… view at source ↗
Figure 5
Figure 5. Figure 5: Randomness extraction and validation for 3 photons BS. a) Von Neumann–unbiased bitstreams. Each row corresponds to one detector channel, showing the final unbiased bitstring obtained after the Von Neumann extractor. The length varies depending on the number of discarded pairs, reflecting statistical fluctuations in the raw data. b) NIST statistical test suite. In the figure, we show the results of the NIST… view at source ↗
read the original abstract

Integrated quantum photonics has emerged as one of the leading platforms for scaling quantum information processing, offering compact, stable, and low-loss hardware with precise phase and mode control. Advances in integrated photonics architectures and active programmability now enable complex, high-dimensional transformations essential for quantum advantage tasks. We introduce an integrated, reconfigurable 3D photonic device with 128 modes for manipulation of single-photon quantum states (Qolossus 3D). Leveraging a continuously coupled architecture and thermo-optic programmability, the platform implements reconfigurable unitary transformations at unprecedented scale for integrated quantum optics. Exploiting indistinguishable single photons demultiplexed from a quantum dot source, we perform Boson Sampling across the large-dimensional chip and analyse the resulting output distributions for up to 4 photons. We then exploit it to demonstrate randomness generation via Boson Sampling. Agreement with theoretical predictions validates both the device's reconfigurable operation and the generation of random numbers. Our results highlight the scalability, stability, and precise control of integrated photonics for quantum information processing.

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 / 3 minor

Summary. The manuscript reports the development of a 128-mode reconfigurable 3D photonic integrated circuit (Qolossus 3D) based on a continuously coupled architecture with thermo-optic phase shifters for implementing programmable unitary transformations. Using single photons demultiplexed from a quantum-dot source, the authors conduct Boson Sampling experiments with 1 to 4 photons, compare the measured output photon distributions to ideal theoretical predictions, and utilize the results to demonstrate certified randomness generation. The agreement between experimental data and theory is presented as evidence for both the successful reconfigurable operation of the device and the validity of the randomness extraction.

Significance. This experimental demonstration of Boson Sampling on a large-scale reconfigurable integrated photonic platform at 128 modes is significant for the field of quantum information processing. It showcases the potential for scaling photonic quantum hardware while maintaining the ability to perform complex transformations and extract useful quantum resources like randomness. The integration of a quantum dot source further highlights a path toward fully integrated quantum photonic systems. Strengths include the scale of the device and the direct application to a quantum advantage task.

major comments (2)
  1. §4 (Boson Sampling results): The central claim of agreement with theoretical predictions for up to 4 photons is load-bearing for validating both reconfigurability and randomness generation, yet the manuscript provides no quantitative metrics (e.g., total variation distance, fidelity, or chi-squared statistics) with error bars derived from repeated measurements or loss characterization; this leaves the weakest assumption on photon indistinguishability and unitary fidelity untested at the level needed to support the conclusions.
  2. §5 (Randomness generation): The exploitation of Boson Sampling output distributions for randomness certification requires explicit description of the statistical test, sample size, and how experimental imperfections (loss, partial distinguishability) are folded into the min-entropy bound; without this, the claim that agreement validates randomness extraction cannot be fully assessed.
minor comments (3)
  1. Abstract: The statement of agreement with theory would be strengthened by a single quantitative figure (e.g., average fidelity or distance) even at the summary level.
  2. Figure captions and methods: Ensure all panels for different photon numbers include the number of experimental runs and the measured two-photon interference visibility used in the theoretical model.
  3. Notation: The definition of the implemented unitary in the continuously coupled architecture should be cross-referenced to the thermo-optic voltage-to-phase calibration curve for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for the constructive comments, which we address point by point below. We will incorporate the suggested quantitative metrics and clarifications in the revised version to strengthen the validation of our results.

read point-by-point responses

  1. Referee: §4 (Boson Sampling results): The central claim of agreement with theoretical predictions for up to 4 photons is load-bearing for validating both reconfigurability and randomness generation, yet the manuscript provides no quantitative metrics (e.g., total variation distance, fidelity, or chi-squared statistics) with error bars derived from repeated measurements or loss characterization; this leaves the weakest assumption on photon indistinguishability and unitary fidelity untested at the level needed to support the conclusions.

    Authors: We agree that quantitative metrics provide a more rigorous validation of the agreement between measured distributions and theoretical predictions. In the revised manuscript, we will include total variation distance and fidelity calculations between the experimental data and ideal Boson Sampling distributions for 1–4 photons, with error bars derived from repeated measurements. We will also integrate loss characterization results to quantify the effects on photon indistinguishability and unitary fidelity, thereby addressing the assumptions underlying our conclusions on reconfigurability. revision: yes

  2. Referee: §5 (Randomness generation): The exploitation of Boson Sampling output distributions for randomness certification requires explicit description of the statistical test, sample size, and how experimental imperfections (loss, partial distinguishability) are folded into the min-entropy bound; without this, the claim that agreement validates randomness extraction cannot be fully assessed.

    Authors: We will expand the description in §5 to explicitly detail the statistical test used for randomness certification, the sample sizes collected from the Boson Sampling experiments, and the precise manner in which experimental imperfections—including photon loss and partial distinguishability—are incorporated into the min-entropy bound. This addition will enable a complete evaluation of the certified randomness claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript is an experimental report on fabricating and operating a 128-mode reconfigurable 3D photonic circuit to implement Boson Sampling with up to four photons. All load-bearing claims consist of measured output statistics being compared to independently computed ideal Boson Sampling distributions; those theoretical distributions are standard and external to the present data set. No equation, fit, or self-citation is shown to define a quantity that is then re-presented as a prediction or uniqueness result derived from the same experiment. The derivation chain therefore remains self-contained and non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, limiting visibility into exact parameters and assumptions; the ledger reflects the minimal set implied by the description.

free parameters (1)
  • thermo-optic phase shifter voltages
    Reconfigurability depends on calibrated voltages to set phases; no specific values or fitting procedure given in abstract.
axioms (1)
  • domain assumption Photons from the quantum dot source are sufficiently indistinguishable for Boson Sampling statistics to apply
    Required for the output distributions to match theoretical predictions as stated.

pith-pipeline@v0.9.0 · 5532 in / 1280 out tokens · 44743 ms · 2026-05-08T17:50:06.406827+00:00 · methodology

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Reference graph

Works this paper leans on

61 extracted references · 6 canonical work pages

  1. [1]

    Aggre- gating T trials forms a T×128 matrix of raw bits which constitutes our entropy source

    that records whether each out- put mode clicked within the acquisition window. Aggre- gating T trials forms a T×128 matrix of raw bits which constitutes our entropy source. Since click probabilities can be mode-dependent (loss, detector efficiency, and coupling asymmetries), the raw matrix is not guaranteed to be unbi- ased or independent across rows/colu...

  2. [2]

    Quantum Glass-based Photonic Integrated Circuits

    which includes 15 tests: the frequency (monobit) test, frequency test within a block, the runs test, test for the longest- run-of-ones in a block, the binary matrix rank test, the Discrete Fourier Transform (DFT) test, the non-overlapping template matching test, the overlapping template matching test, Mau- rer’s ”universal statistical” test, the linear co...

    2022

  3. [3]

    J. Wang, F. Sciarrino, A. Laing, and M. G. Thompson, Nature Photonics14, 273 (2020)

    2020

  4. [4]

    Pelucchi, G

    E. Pelucchi, G. Fagas, I. Aharonovich, D. Englund, E. Figueroa, Q. Gong, H. Hannes, J. Liu, C.-Y . Lu, N. Matsuda, J.-W. Pan, F. Schreck, F. Sciarrino, C. Silberhorn, J. Wang, and K. D. J¨ons, Nature Reviews Physics4, 194–208 (2021)

    2021

  5. [5]

    Giordani, F

    T. Giordani, F. Hoch, G. Carvacho, N. Spagnolo, and F. Sciar- rino, La Rivista del Nuovo Cimento46, 71–103 (2023)

    2023

  6. [6]

    Aaronson and A

    S. Aaronson and A. Arkhipov, inProceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC ’11 (Association for Computing Machinery, New York, NY , USA,

  7. [7]

    D. J. Brod, E. F. Galv˜ao, A. Crespi, R. Osellame, N. Spagnolo, and F. Sciarrino, Advanced Photonics1, 034001 (2019)

    2019

  8. [8]

    J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, Nat. Photon.9, 615 (2015)

    2015

  9. [9]

    T. R. Bromley, J. M. Arrazola, S. Jahangiri, J. Izaac, N. Que- sada, A. D. Gran, M. Schuld, J. Swinarton, Z. Zabaneh, and N. Killoran, Quantum Sci. Technol.5, 034010 (2020)

    2020

  10. [10]

    Chabaud, D

    U. Chabaud, D. Markham, and A. Sohbi, Quantum5, 496 (2021)

    2021

  11. [11]

    Edelman and N

    A. Edelman and N. R. Rao, Acta Numerica14, 233–297 (2005)

    2005

  12. [12]

    M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, Science339, 794 (2013)

    2013

  13. [13]

    J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Lang- ford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, Science339, 798 (2013)

    2013

  14. [14]

    Crespi, R

    A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galv˜ao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciar- rino, Nature Photonics7, 545 (2013)

    2013

  15. [15]

    Tillmann, B

    M. Tillmann, B. Daki´c, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, Nature Photonics7, 540 (2013)

    2013

  16. [16]

    J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White, Phys. Rev. Lett.118, 130503 (2017). 7

    2017

  17. [17]

    Y . He, X. Ding, Z.-E. Su, H.-L. Huang, J. Qin, C. Wang, S. Unsle- ber, C. Chen, H. Wang, Y .-M. He, X.-L. Wang, W.-J. Zhang, S.-J. Chen, C. Schneider, M. Kamp, L.-X. You, Z. Wang, S. H¨ofling, C.-Y . Lu, and J.-W. Pan, Phys. Rev. Lett.118, 190501 (2017)

    2017

  18. [18]

    H. Wang, Y . He, Y .-H. Li, Z.-E. Su, B. Li, H.-L. Huang, X. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y .-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. H ¨ofling, C.-Y . Lu, and J.-W. Pan, Nature Photonics11, 361 (2017)

    2017

  19. [19]

    Zhong, Y

    H.-S. Zhong, Y . Li, W. Li, L.-C. Peng, Z.-E. Su, Y . Hu, Y .-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y .-A. Chen, N.-L. Liu, C.-Y . Lu, and J.-W. Pan, Phys. Rev. Lett.121, 250505 (2018)

    2018

  20. [20]

    Arriola, S

    A. Arriola, S. Gross, N. Jovanovic, N. Charles, P. G. Tuthill, S. M. Olaizola, A. Fuerbach, and M. J. Withford, Opt. Express 21, 2978 (2013)

    2013

  21. [21]

    F. Hoch, S. Piacentini, T. Giordani, Z.-N. Tian, M. Iuliano, C. Es- posito, A. Camillini, G. Carvacho, F. Ceccarelli, N. Spagnolo, A. Crespi, F. Sciarrino, and R. Osellame, npj Quantum Informa- tion8, 55 (2022)

    2022

  22. [22]

    Zhou, X.-W

    W.-H. Zhou, X.-W. Wang, R.-J. Ren, Y .-X. Fu, Y .-J. Chang, X.-Y . Xu, H. Tang, and X.-M. Jin, Light: Science & Applications13, 296 (2024)

    2024

  23. [23]

    Youssry, Y

    A. Youssry, Y . Yang, R. J. Chapman, B. Haylock, F. Lenzini, M. Lobino, and A. Peruzzo, npj Quantum Information10, 9 (2024)

    2024

  24. [24]

    Y . Yang, R. J. Chapman, B. Haylock, F. Lenzini, Y . N. Joglekar, M. Lobino, and A. Peruzzo, Nature Communications15, 50 (2024)

    2024

  25. [25]

    Y . Yang, R. J. Chapman, A. Youssry, B. Haylock, F. Lenzini, M. Lobino, and A. Peruzzo, npj Quantum Information11, 19 (2025)

    2025

  26. [26]

    Zhong, H

    H.-S. Zhong, H. Wang, Y .-H. Deng, M.-C. Chen, L.-C. Peng, Y .-H. Luo, J. Qin, D. Wu, X. Ding, Y . Hu, P. Hu, X.-Y . Yang, W.-J. Zhang, H. Li, Y . Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, C.-Y . Lu, and J.-W. Pan, Science370, 1460–1463 (2020)

    2020

  27. [27]

    Zhong, Y .-H

    H.-S. Zhong, Y .-H. Deng, J. Qin, H. Wang, M.-C. Chen, L.-C. Peng, Y .-H. Luo, D. Wu, S.-Q. Gong, H. Su, Y . Hu, P. Hu, X.-Y . Yang, W.-J. Zhang, H. Li, Y . Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N.-L. Liu, J. J. Renema, C.-Y . Lu, and J.-W. Pan, Physical Review Letters127, 180502 (2021)

    2021

  28. [28]

    L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vin- cent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. E. Lita, T. Gerrits, S. W. Nam, V . D. Vaidya, M. Menotti, I. Dhand, Z. Vernon, N. Quesada, and J. Lavoie, Nature606, 75–81 (2022)

    2022

  29. [29]

    Deng, Y .-C

    Y .-H. Deng, Y .-C. Gu, H.-L. Liu, S.-Q. Gong, H. Su, Z.-J. Zhang, H.-Y . Tang, M.-H. Jia, J.-M. Xu, M.-C. Chen, J. Qin, L.-C. Peng, J. Yan, Y . Hu, J. Huang, H. Li, Y . Li, Y . Chen, X. Jiang, L. Gan, G. Yang, L. You, L. Li, H.-S. Zhong, H. Wang, N.-L. Liu, J. J. Renema, C.-Y . Lu, and J.-W. Pan, Physical Review Letters131, 150601 (2023)

    2023

  30. [30]

    Robust quantum computational advantage with programmable 3050- photon gaussian boson sampling,

    H.-L. Liu, H. Su, S.-Q. Gong, Y .-C. Gu, H.-Y . Tang, M.-H. Jia, Q. Wei, Y . Song, D. Wang, M. Zheng, F. Chen, L. Li, S. Ren, X. Zhu, M. Wang, Y . Chen, Y . Liu, L. Song, P. Yang, J. Chen, H. An, L. Zhang, L. Gan, G. Yang, J.-M. Xu, Y .-M. He, H. Wang, H.-S. Zhong, M.-C. Chen, X. Jiang, L. Li, N.-L. Liu, Y .-H. Deng, X.-L. Su, Q. Zhang, C.-Y . Lu, and J.-...

    work page arXiv 2025

  31. [31]

    R. B. Patel, T. Rudolph, and G. J. Pryde, Science Advances5, eaau6668 (2019)

    2019

  32. [32]

    F. Hoch, T. Giordani, L. Castello, G. Carvacho, N. Spagnolo, F. Ceccarelli, C. Pentangelo, S. Piacentini, A. Crespi, R. Osel- lame, E. F. Galv˜ao, and F. Sciarrino, Nature Photonics19, 12–19 (2024)

    2024

  33. [33]

    Rodari, F

    G. Rodari, F. Hoch, A. Suprano, T. Giordani, E. Negro, G. Car- vacho, N. Spagnolo, E. F. Galv ˜ao, and F. Sciarrino, Science Advances10, eado6244 (2024)

    2024

  34. [34]

    M. C. Anguita, T. Roelink, S. Marzban, W. Briels, C. Filippi, and J. Renema, (2025), arXiv:2509.25404 [quant-ph]

    work page arXiv 2025

  35. [35]

    J. Shi, T. Zhao, Y . Wang, C. Yu, Y . Lu, J. Wu, R. Shi, S. Zhang, S. Peng, and J. Wu, Advanced Quantum Technologies7, 2300179 (2024)

    2024

  36. [36]

    Ange and M

    J. Ange and M. A. Thornton, inQuantum Information Science, Sensing, and Computation XVII, V ol. 13451, edited by M. Hay- duk, M. L. Fanto, and C. M. T. Jr., International Society for Optics and Photonics (SPIE, 2025) p. 1345106

    2025

  37. [37]

    Gisin, G

    N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys.74, 145 (2002)

    2002

  38. [38]

    Pirandola, U

    S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V . C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Adv. Opt. Photon.12, 1012 (2020)

    2020

  39. [39]

    Portmann and R

    C. Portmann and R. Renner, Rev. Mod. Phys.94, 025008 (2022)

    2022

  40. [40]

    Dubrov and Y

    B. Dubrov and Y . Ishai, inProceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’06 (Association for Computing Machinery, New York, NY , USA,

  41. [41]

    Zhuang, X

    D. Zhuang, X. Zhang, S. Song, and S. Hooker, inProceedings of Machine Learning and Systems, V ol. 4, edited by D. Marculescu, Y . Chi, and C. Wu (2022) pp. 316–336

    2022

  42. [42]

    Scardapane and D

    S. Scardapane and D. Wang, WIREs Data Mining and Knowl- edge Discovery7, e1200 (2017)

    2017

  43. [43]

    L. Li, M. Cai, T. Wang, Z. Tan, P. Huang, K. Wu, and G. Zeng, Photon. Res.12, 1379 (2024)

    2024

  44. [44]

    A high speed integrated quantum random num- ber generator with on-chip real-time randomness extraction,

    F. Regazzoni, E. Amri, S. Burri, D. Rusca, H. Zbinden, and E. Charbon, “A high speed integrated quantum random num- ber generator with on-chip real-time randomness extraction,” (2021), arXiv:2102.06238 [quant-ph]

    work page arXiv 2021

  45. [45]

    Abellan, W

    C. Abellan, W. Amaya, D. Domenech, P. M. noz, J. Capmany, S. Longhi, M. W. Mitchell, and V . Pruneri, Optica3, 989 (2016)

    2016

  46. [46]

    T. K. Para¨ıso, T. Roger, D. G. Marangon, I. De Marco, M. San- zaro, R. I. Woodward, J. F. Dynes, Z. Yuan, and A. J. Shields, Nature Photonics15, 850 (2021)

    2021

  47. [47]

    B. Bai, J. Huang, G.-R. Qiao, Y .-Q. Nie, W. Tang, T. Chu, J. Zhang, and J.-W. Pan, Applied Physics Letters118, 264001 (2021)

    2021

  48. [48]

    Bruynsteen, T

    C. Bruynsteen, T. Gehring, C. Lupo, J. Bauwelinck, and X. Yin, PRX Quantum4, 010330 (2023), arXiv:2209.04339 [quant-ph]

    work page arXiv 2023

  49. [49]

    D. G. Marangon, P. R. Smith, N. Walk, T. K. Para¨ıso, J. F. Dynes, V . Lovic, M. Sanzaro, T. Roger, I. De Marco, M. Lucamarini, Z. Yuan, and A. J. Shields, Nature Electronics7, 396–404 (2024)

    2024

  50. [50]

    Aaronson and A

    S. Aaronson and A. Arkhipov, Quantum Info. Comput.14, 1383–1423 (2014)

    2014

  51. [51]

    Spagnolo, C

    N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galv˜ao, and F. Sciarrino, Nature Photonics 8, 615–620 (2014)

    2014

  52. [52]

    Elben, S

    A. Elben, S. T. Flammia, H.-Y . Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, Nature Reviews Physics5, 9–24 (2022)

    2022

  53. [53]

    O. Lib, S. Liu, R. Shekel, Q. He, M. Huber, Y . Bromberg, and G. Vitagliano, Phys. Rev. Lett.134, 210202 (2025). 8

    2025

  54. [54]

    Laing and J

    A. Laing and J. L. O’Brien, “Super-stable tomography of any linear optical device,” (2012), arXiv:1208.2868 [quant-ph]

    work page arXiv 2012

  55. [55]

    Bassham, A

    L. Bassham, A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks,et al., A statistical test suite for random and pseudorandom number generators for cryptographic applications, Tech. Rep. (National Institute of Standards and Technology, 2008)

    2008

  56. [56]

    Singh, G

    D. Singh, G. Muraleedharan, B. Fu, C.-M. Cheng, N. Roussy Newton, P. P. Rohde, and G. K. Brennen, Quan- tum Science and Technology10, 025020 (2025)

    2025

  57. [57]

    H. Dale, D. Jennings, and T. Rudolph, Nature communications 6, 8203 (2015)

    2015

  58. [58]

    Jiang, J

    J. Jiang, J. Zhang, and X. Sun, Phys. Rev. A97, 032303 (2018)

    2018

  59. [59]

    Complexity and multi-functional variants of the quantum- to-quantum bernoulli factories,

    F. Hoch, T. Giordani, G. Carvacho, N. Spagnolo, and F. Sciar- rino, “Complexity and multi-functional variants of the quantum- to-quantum bernoulli factories,” (2025), arXiv:2512.10810 [quant-ph]

    work page arXiv 2025

  60. [60]

    Kashefi and A

    E. Kashefi and A. Pappa, Cryptography1, 12 (2017)

    2017

  61. [61]

    M. Yan, C. Huang, P. Bienstman, P. Tino, W. Lin, and J. Sun, Nature Communications15, 2056 (2024)

    2056