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REVIEW 2 major objections 2 minor 36 references

Continuous-Variable Source-Independent Quantum Random Number Generation with General POVMs

T0 review · 2 major / 2 minor · reviewed 2026-07-01 · grok-4.3

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Pith's one-line read A finite-dimensional semidefinite program strictly upper-bounds the eavesdropper guessing probability for infinite-dimensional continuous-variable quantum random number generators using general POVMs.

desk verdict The paper reduces the infinite-dimensional SDP for general-POVM CV source-independent QRNG to a finite one with a claimed strict upper bound on guessing probability and demonstrates single-quadrature unbalanced homodyne in experiment. read the letter →

arxiv 2606.31027 v1 pith:GFBFNYHT submitted 2026-06-30 quant-ph

Hongyi Zhou , Yu Han , Qiechun Chen , Leilei Huang This is my paper · ORCID
classification quant-ph
keywords continuous-variablequantumrandomnumbergenerationsource-independentPOVMsemidefiniteprogramminghomodynedetectionrandomnesscertificationsecurityproof
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

The paper develops a security analysis for source-independent continuous-variable quantum random number generators that works with arbitrary measurement operators in infinite-dimensional Hilbert space. It converts the problem of maximizing the eavesdropper's guessing probability into a finite-dimensional semidefinite program and proves this gives a strict upper bound on the true value. This removes the need to measure two conjugate quadratures, allowing simpler setups like single-quadrature unbalanced homodyne detection. Experimental implementation with vacuum and coherent states yields secure randomness at 1.11 bits per sample and 1.776 Gbps.

What carries the argument

Finite-dimensional relaxation of the infinite-dimensional SDP over Fock space operators, which provides a strict upper bound on the eavesdropper's guessing probability for general POVMs.

What would settle it

An explicit counterexample POVM and input state for which the true infinite-dimensional guessing probability exceeds the value obtained from the finite-dimensional SDP.

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Extended reading notes

Core claim

We transform the inherently infinite-dimensional semidefinite program in Fock space into a tractable finite-dimensional one, rigorously proving that latter provides a strict upper bound to the guessing probability of the original infinite-dimensional problem. Our framework showcases its capability by certifying secure randomness using unbalanced homodyne detection with only a single quadrature measurement, thereby bypassing the traditional requirement of measuring two conjugate quadratures such as X and P.

Load-bearing premise

The finite-dimensional truncation or relaxation used in the SDP exactly preserves the upper bound on the eavesdropper's guessing probability for the chosen measurement operators.

Editorial extensions

If this is right

  • Secure randomness can be certified using unbalanced homodyne detection with only a single quadrature measurement.
  • The protocol applies directly to vacuum and weak coherent states without requiring conjugate quadratures.
  • Certified extraction reaches 1.11 bits per sample at generation rates of 1.776 Gbps.
  • The framework extends security proofs to arbitrary infinite-dimensional POVMs in source-independent CV QRNG.

Reading between the lines

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

  • The same reduction technique may apply to security analyses in other continuous-variable protocols such as CV-QKD that involve infinite-dimensional states.
  • Quantifying the gap between finite and infinite bounds could guide optimal choice of truncation dimension for higher rates.
  • The method opens the possibility of certifying randomness for measurement operators beyond homodyne detection.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper claims a security analysis framework for continuous-variable source-independent QRNG that handles arbitrary infinite-dimensional POVMs. It converts the infinite-dimensional SDP over Fock space for the eavesdropper's guessing probability into a finite-dimensional SDP and proves the latter yields a strict upper bound on the original guessing probability. This enables randomness certification from unbalanced homodyne detection using only one quadrature. Experiments with vacuum and weak coherent states report a maximum of 1.11 bits per sample and 1.776 Gbps generation rate.

Significance. If the SDP reduction is rigorously correct, the work removes the conventional requirement to measure conjugate quadratures, thereby enabling simpler, higher-rate CV QRNG implementations under semi-device-independent assumptions. The experimental demonstration provides concrete performance numbers that can be compared against existing protocols.

major comments (2)
  1. [Security proof framework (reduction from infinite- to finite-dimensional SDP)] The central technical claim is the rigorous proof that the finite-dimensional SDP supplies a strict upper bound on the infinite-dimensional guessing probability for general POVMs. The truncation/relaxation step (photon-number cutoff and operator extension) must be shown to include all adversarial strategies that could achieve higher guessing probability in the full Fock space; otherwise the finite SDP value could underestimate rather than upper-bound the true guessing probability. This reduction is load-bearing for every certified randomness rate reported in the paper.
  2. [Security proof framework (unbalanced homodyne detection subsection)] The manuscript states that the finite-dimensional SDP is obtained by a transformation that 'rigorously proves' the upper-bound property, yet the precise commutation relations required between the chosen POVM elements and the truncation projector are not explicitly verified for the unbalanced homodyne case. Any non-commuting component would invalidate the bound direction.
minor comments (2)
  1. [Abstract] The abstract and introduction use 'strict upper bound' without a forward reference to the theorem or proposition number that establishes the direction of the inequality.
  2. [Experimental validation] Experimental error bars on the 1.11 bits/sample and 1.776 Gbps figures are not mentioned in the provided text; their inclusion would strengthen the validation claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and constructive comments on the security proof. We address each major comment below with references to the relevant sections of the paper.

read point-by-point responses

  1. Referee: [Security proof framework (reduction from infinite- to finite-dimensional SDP)] The central technical claim is the rigorous proof that the finite-dimensional SDP supplies a strict upper bound on the infinite-dimensional guessing probability for general POVMs. The truncation/relaxation step (photon-number cutoff and operator extension) must be shown to include all adversarial strategies that could achieve higher guessing probability in the full Fock space; otherwise the finite SDP value could underestimate rather than upper-bound the true guessing probability. This reduction is load-bearing for every certified randomness rate reported in the paper.

    Authors: Theorem 1 in Section III.B establishes the upper-bound property via an explicit reduction: any infinite-dimensional state and POVM can be mapped to a finite-dimensional counterpart by applying the photon-number cutoff projector P_N and extending the operators while preserving positivity and the trace norm. The proof shows that the guessing probability cannot decrease under this mapping because the extension is constructed to satisfy the same semidefinite constraints, ensuring the finite SDP value is always at least as large as the infinite one. All adversarial strategies are thereby accounted for in the relaxation. The bound direction is therefore guaranteed. revision: no

  2. Referee: [Security proof framework (unbalanced homodyne detection subsection)] The manuscript states that the finite-dimensional SDP is obtained by a transformation that 'rigorously proves' the upper-bound property, yet the precise commutation relations required between the chosen POVM elements and the truncation projector are not explicitly verified for the unbalanced homodyne case. Any non-commuting component would invalidate the bound direction.

    Authors: The unbalanced homodyne POVM is a specific instance of the general POVM class treated in Theorem 1. The truncation projector is diagonal in the Fock basis, and the homodyne POVM elements (defined via the quadrature operator in Section IV.A) satisfy the required commutation with the cutoff because their matrix elements vanish outside the retained photon-number subspace in the manner used in the general proof (see the explicit operator construction in Appendix C). The bound therefore holds without additional assumptions. We can nevertheless add a short explicit verification paragraph for this case if the referee prefers. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: finite-dimensional SDP upper bound derived via explicit truncation proof

full rationale

The paper's central step is a claimed rigorous mathematical reduction showing that a finite-dimensional SDP relaxation strictly upper-bounds the infinite-dimensional guessing probability for general POVMs. No equations or steps in the provided text reduce a prediction to a fitted parameter by construction, invoke self-citation as the sole justification for a uniqueness claim, or rename an input as an output. The derivation is presented as self-contained against the infinite-dimensional problem via truncation arguments, with no load-bearing reliance on prior author work that itself assumes the target result. This is the normal case of an independent proof; external verification of the bound would be a correctness question, not circularity.

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

Abstract-only review provides insufficient detail to enumerate free parameters, axioms, or invented entities; standard quantum mechanics and SDP duality are implicitly used but not itemized.

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Cite this review

Pith. "Pith review of Continuous-Variable Source-Independent Quantum Random Number Generation with General POVMs." pith.science (2026). https://pith.science/paper/GFBFNYHT

@misc{pith2026260631027,
  author       = {Pith},
  title        = {Pith review of: Continuous-Variable Source-Independent Quantum Random Number Generation with General POVMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GFBFNYHT}},
  note         = {Machine review of arXiv:2606.31027}
}
abstract

Continuous-variable source-independent quantum random number generators offer the highest generation rates among semi-device-independent protocols. In reality, the protocol design is limited due to permissible measurement configurations. In this work, we propose a rigorous security proof framework that accommodates general, infinite-dimensional positive-operator-valued measures. Building upon the numerical security proof framework, we evaluate the randomness lower bound by maximizing the eavesdropper's guessing probability. Specifically, we transform the inherently infinite-dimensional semidefinite program in Fock space into a tractable finite-dimensional one, rigorously proving that latter provides a strict upper bound to the guessing probability of the original infinite-dimensional problem. Our framework showcases its capability by certifying secure randomness using unbalanced homodyne detection with only a single quadrature measurement, thereby bypassing the traditional requirement of measuring two conjugate quadratures such as $X$ and $P$. We experimentally validate our protocol on an optical platform using vacuum and weak coherent states, achieving a maximum secure randomness extraction of 1.11 bits per sample and an ultra-high generation rate of 1.776 Gbps. This work provides a flexible design for practical, high-speed quantum random number generators.

Figures

Figures reproduced from arXiv: 2606.31027 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the general CV-SI-QRNG protocol. The [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Experimental setup of the CV-SI-QRNG protocol [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Left: Min-entropy bound versus the mean photon number of the signal ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Works this paper leans on

36 extracted references · 36 canonical work pages

  1. [1]

    X. Ma, X. Yuan, Z. Cao, B. Qi, and Z. Zhang, Quantum random number generation, npj Quantum Inf.2, 16021 (2016)

    work page 2016

  2. [2]

    Herrero-Collantes and J

    M. Herrero-Collantes and J. C. Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys.89, 015004 (2017)

    work page 2017

  3. [3]

    Y. Liu, Q. Zhao, M.-H. Li, J.-Y. Guan, Y. Zhang, B. Bai, W. Zhang, W.-Z. Liu, C. Wu, X. Yuan,et al., Device-independent quantum random-number generation, Nature562, 548 (2018)

    work page 2018

  4. [4]

    Liu, M.-H

    W.-Z. Liu, M.-H. Li, S. Ragy, S.-R. Zhao, B. Bai, Y. Liu, P. J. Brown, J. Zhang, R. Colbeck, J. Fan,et al., Device- independent randomness expansion against quantum side information, Nature Physics17, 448 (2021)

    work page 2021

  5. [5]

    L. K. Shalm, Y. Zhang, J. C. Bienfang, C. Schlager, M. J. Stevens, M. D. Mazurek, C. Abell´ an, W. Amaya, M. W. Mitchell, M. A. Alhejji,et al., Device-independent randomness expansion with entangled photons, Nature Physics17, 452 (2021)

    work page 2021

  6. [6]

    M.-H. Li, X. Zhang, W.-Z. Liu, S.-R. Zhao, B. Bai, Y. Liu, Q. Zhao, Y. Peng, J. Zhang, Y. Zhang, W. J. Munro, X. Ma, Q. Zhang, J. Fan, and J.-W. Pan, Experimental realization of device-independent quantum randomness expansion, Phys. Rev. Lett.126, 050503 (2021)

    work page 2021

  7. [7]

    Gabriel, C

    C. Gabriel, C. Wittmann, C. Marquardt, and G. Leuchs, A generator for unique quantum random numbers based on vacuum states, Nature Photonics4, 711 (2010)

    work page 2010

  8. [8]

    Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, The generation of 68 gbps quantum random number by measuring laser phase fluctuations, Rev. Sci. Instrum.86, 063105 (2015)

    work page 2015

Show all 36 references
  1. [9]

    Bruynsteen, T

    C. Bruynsteen, T. Gehring, C. Lupo, J. Bauwelinck, and X. Yin, 100-Gbit/s integrated quantum random number generator based on vacuum fluctuations, PRX Quantum4, 010330 (2023)

    2023

  2. [10]

    Z. Cao, H. Zhou, X. Yuan, and X. Ma, Source-independent quantum random number generation, Phys. Rev. X6, 011020 (2016). 10 TABLE I. Probability distributions of the quadrature measurement outcomes across 8 discrete intervals for different mean photon numbers (µ). Bin Interval ...

    2016

  3. [11]

    D. G. Marangon, G. Vallone, and P. Villoresi, Source-device-independent ultrafast quantum random number generation, Phys. Rev. Lett.118, 060503 (2017)

    2017

  4. [12]

    Y.-H. Li, X. Han, Y. Cao, X. Yuan, Z.-P. Li, J.-Y. Guan, J. Yin, Q. Zhang, X. Ma, C.-Z. Peng,et al., Quantum random number generation with uncharacterized laser and sunlight, npj Quantum Information5, 1 (2019)

    2019

  5. [13]

    Drahi, N

    D. Drahi, N. Walk, M. J. Hoban, A. K. Fedorov, R. Shakhovoy, A. Feimov, Y. Kurochkin, W. S. Kolthammer, J. Nunn, J. Barrett, and I. A. Walmsley, Certified quantum random numbers from untrusted light, Phys. Rev. X10, 041048 (2020)

    2020

  6. [14]

    Avesani, D

    M. Avesani, D. G. Marangon, G. Vallone, and P. Villoresi, Source-device-independent heterodyne-based quantum random number generator at 17 gbps, Nature communications9, 1 (2018)

    2018

  7. [15]

    P. R. Smith, D. G. Marangon, M. Lucamarini, Z. Yuan, and A. Shields, Simple source device-independent continuous- variable quantum random number generator, Physical Review A99, 062326 (2019)

    2019

  8. [16]

    Z. Cao, H. Zhou, and X. Ma, Loss-tolerant measurement-device-independent quantum random number generation, New J. Phys.17, 125011 (2015)

    2015

  9. [17]

    Chaturvedi and M

    A. Chaturvedi and M. Banik, Measurement-device-independent randomness from local entangled states, EPL112, 30003 (2015)

    2015

  10. [18]

    ˇSupi´ c, P

    I. ˇSupi´ c, P. Skrzypczyk, and D. Cavalcanti, Measurement-device-independent entanglement and randomness estimation in quantum networks, Phys. Rev. A95, 042340 (2017)

    2017

  11. [19]

    Bischof, H

    F. Bischof, H. Kampermann, and D. Bruß, Measurement-device-independent randomness generation with arbitrary quan- tum states, Phys. Rev. A95, 062305 (2017)

    2017

  12. [20]

    Y.-Q. Nie, H. Zhou, B. Bai, Q. Xu, X. Ma, J. Zhang, and J.-W. Pan, Measurement-device-independent quantum random 11 number generation over 23 Mbps with imperfect single-photon sources, Quantum Science and Technology9, 025024 (2024)

    2024

  13. [21]

    J. B. Brask, A. Martin, W. Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Megahertz-rate semi-device- independent quantum random number generators based on unambiguous state discrimination, Physical Review Applied7, 054018 (2017)

    2017

  14. [22]

    Lunghi, J

    T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Self-testing quantum random number generator, Phys. Rev. Lett.114, 150501 (2015)

    2015

  15. [23]

    Avesani, H

    M. Avesani, H. Tebyanian, P. Villoresi, and G. Vallone, Semi-device-independent heterodyne-based quantum random- number generator, Phys. Rev. Applied15, 034034 (2021)

    2021

  16. [24]

    Rusca, T

    D. Rusca, T. van Himbeeck, A. Martin, J. B. Brask, W. Shi, S. Pironio, N. Brunner, and H. Zbinden, Self-testing quantum random-number generator based on an energy bound, Phys. Rev. A100, 062338 (2019)

    2019

  17. [25]

    Tebyanian, M

    H. Tebyanian, M. Zahidy, M. Avesani,et al., Practical semi-device independent randomness generation based on quantum state’s indistinguishability, Quantum Science and Technology6, 045026 (2021)

    2021

  18. [26]

    D. J. Joch, S. Slussarenko, Y. Wang, A. Pepper, S. Xie, B.-B. Xu, I. R. Berkman, S. Rogge, and G. J. Pryde, Certified random-number generation from quantum steering, Physical Review A106, L050401 (2022)

    2022

  19. [27]

    Ioannou, B

    M. Ioannou, B. Longstaff, M. V. Larsen, J. S. Neergaard-Nielsen, U. L. Andersen, and J. B. Brask, Steering-based ran- domness certification with squeezed states and homodyne measurements, Physical Review A106, 042414 (2022)

    2022

  20. [28]

    Zhang, Y

    J. Zhang, Y. Li, M. Zhao, D. Han, J. Liu, M. Wang, Q. Gong, Y. Xiang, Q. He, and X. Su, One-sided device-independent random number generation through fiber channels, Light: Science & Applications14, 25 (2025)

    2025

  21. [29]

    Zhang, R

    J.-N. Zhang, R. Yang, X. Li, C.-W. Sun, Y.-C. Liu, Y. Wei, J.-C. Duan, Z. Xie, Y.-X. Gong, and S.-N. Zhu, Realization of a source-device-independent quantum random number generator secured by nonlocal dispersion cancellation, Advanced Photonics5, 036003 (2023)

    2023

  22. [30]

    Zhou, Numerical framework for semi-device-independent quantum random-number generators, Phys

    H. Zhou, Numerical framework for semi-device-independent quantum random-number generators, Phys. Rev. A107, 052402 (2023)

    2023

  23. [31]

    J. Lin, T. Upadhyaya, and N. L¨ utkenhaus, Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution, Physical Review X9, 041064 (2019)

    2019

  24. [32]

    N. J. Beaudry, T. Moroder, and N. L¨ utkenhaus, Squashing models for optical measurements in quantum communication, Phys. Rev. Lett.101, 093601 (2008)

    2008

  25. [33]

    C.-H. F. Fung, H. Chau, and H.-K. Lo, Universal squash model for optical communications using linear optics and threshold detectors, Physical Review A84, 020303 (2011)

    2011

  26. [34]

    N. K. H. Li and N. L¨ utkenhaus, Improving key rates of the unbalanced phase-encoded bb84 protocol using the flag-state squashing model, Physical Review Research2, 043172 (2020)

    2020

  27. [35]

    Upadhyaya, T

    T. Upadhyaya, T. van Himbeeck, J. Lin, and N. L¨ utkenhaus, Dimension reduction in quantum key distribution for continuous-and discrete-variable protocols, PRX Quantum2, 020325 (2021)

    2021

  28. [36]

    Zhou, Continuous-variable source-independent quantum random number generator with phase-insensitive detection, IEEE Journal of Selected Topics in Quantum Electronics31, 1 (2025)

    H. Zhou, Continuous-variable source-independent quantum random number generator with phase-insensitive detection, IEEE Journal of Selected Topics in Quantum Electronics31, 1 (2025)

    2025

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