Genuine certifiable randomness from a black-box

Liam P. McGuinness

arxiv: 2603.00401 · v3 · submitted 2026-02-28 · 🪐 quant-ph · math-ph· math.MP

Genuine certifiable randomness from a black-box

Liam P. McGuinness This is my paper

Pith reviewed 2026-05-15 19:01 UTC · model grok-4.3

classification 🪐 quant-ph math-phmath.MP

keywords quantum randomnessblack-box certificationsingle-particle statesrandomness generationdevice-independent protocols

0 comments

The pith

Single-particle quantum measurements certify genuine randomness in a fully black-box setting without any initial seed.

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

The paper shows that measurements performed on single quantum particles suffice to certify that the output data is genuinely random. In this black-box approach, the certification procedure rejects any data that could have been produced by a deterministic process, even if the adversary knows the full protocol and has unlimited power. The method requires no trusted device model and starts with no random seed, which removes the usual circularity in randomness generation. This matters because it allows untrusted hardware to produce numbers that pass a test no classical simulation can fake.

Core claim

Randomness can be certified in the black-box setting by applying a certification test to outcomes obtained solely from measurements on single-particle quantum states, without any initial random seed and without assumptions on the internal workings of the apparatus.

What carries the argument

The black-box certification test applied to measurement outcomes from single-particle states, which rejects all deterministic data while accepting quantum randomness.

If this is right

Provably random bits can be extracted using only single-particle sources and standard measurements.
No pre-shared random seed is required to start the certification process.
The protocol remains secure against any deterministic adversary regardless of computational power.
Randomness generation becomes possible with devices whose internal physics need not be characterized.

Where Pith is reading between the lines

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

The approach may simplify the hardware needed for device-independent random number generators.
Similar certification could apply to other single-particle protocols such as quantum key distribution.
Experimental tests on actual single-particle systems would provide a direct check of the certification threshold.

Load-bearing premise

That the statistical properties of single-particle measurement outcomes alone are sufficient to distinguish any deterministic classical process from genuine quantum randomness.

What would settle it

Exhibiting a deterministic classical algorithm that produces outcome statistics passing the certification test for single-particle measurements would disprove the claim.

Figures

Figures reproduced from arXiv: 2603.00401 by Liam P. McGuinness.

**Figure 1.** Figure 1: (Quantum) estimation certified randomness (ECR). (a) One round of ECR involves: i) the verifier choosing a value of θ and encoding it into a quantum state |θ⟩, ii) sending |θ⟩ to the prover, iii) the prover returning an estimate ˆθ of θ which may or may not derive from a measurement of |θ⟩, iv) the verifier testing the received estimate. (b) A mapping of the parameter θ to the quantum phase of a qubit, thi… view at source ↗

**Figure 2.** Figure 2: Demonstration of non-remote estimation certified randomness with a single NV centre in diamond. (a) After selecting a value of θ, the verifier prepares the NV spin state: |θ⟩ = √ 1 2 (|↑⟩ + exp [−iπθ] |↓⟩) by applying a resonant microwave π/2-pulse with phase π ×θ. The prover performs an X-basis measurement of |θ⟩ by applying a second π/2-pulse with phase π × φ = 0 and projectively reading out the spin-sta… view at source ↗

**Figure 3.** Figure 3: Experimentally testing the randomness of data. The estimate mean squared error as a function of the number of ECR rounds when the verifier uniformly selected θ from Θ6 := {0, 1, 2, 3, 4, 5}/3 and the prover returned a one-bit estimate ˆθ based on four different strategies. (a) The prover’s estimate is the outcome of a measurement |Xx |θ⟩|2 with a ∼ 0.5, b ∼ 0.1 (light green) or a simulation of an ideal mea… view at source ↗

read the original abstract

Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is truly random. However, existing demonstrations are not black-box, to avoid falsely certifying deterministic data, assumptions must be made on how the data was generated. Here we demonstrate genuine randomness certification in the black-box setting -- one in which no deterministic adversary, even with unlimited computational power, will succeed in getting their data certified. We use it to provably generate random numbers using only measurements on single particle states and without a random seed.

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.

Desk Editor's Note private letter to a colleague

The paper claims black-box randomness certification from single-particle states without a seed, but this cannot work because single systems lack the non-local correlations needed to bound deterministic adversaries.

read the letter

The main point is that this paper asserts genuine black-box randomness certification using only measurements on single-particle states and no initial seed. If the protocol actually delivered that, it would simplify quantum random number generators considerably by dropping entanglement and trusted assumptions. The abstract positions it as a demonstration where no deterministic adversary with unlimited power can get bad data certified, which sets it apart from standard device-independent methods that rely on Bell tests with entangled pairs. That attempt at a simpler setup is the clearest new element here. The paper does a reasonable job framing the practical motivation for removing seeds and multi-particle requirements in QRNG contexts. The central soft spot is that the claim runs into a basic limit: single-particle outcomes can always be reproduced by a deterministic adversary who simply emits a fixed sequence or a function of any non-random input, with no Bell violation available to bound the adversary's predictive power. The stress-test concern lands directly on the abstract's premise, and nothing in the description shows a workaround that preserves the black-box guarantee. Without derivations or data in the provided material, the soundness cannot be checked, but the weakest assumption—that single-particle measurements suffice for this certification—does not appear supported by existing theory on device-independent randomness. The citation pattern is not visible, but the overall argument looks overextended relative to what single-system quantum mechanics can certify. This is the kind of paper a reading group might discuss to clarify the gap, but it is not one I would cite or recommend for serious refereeing. The authors would need to supply a concrete mechanism that evades the deterministic-adversary issue before it merits peer review.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to demonstrate genuine randomness certification in a fully black-box setting, where no deterministic adversary with unlimited computational power can produce certifiable data. It asserts that this is achieved using only measurements on single-particle states and without requiring an initial random seed for measurement choices.

Significance. If the central claim were valid, the result would be highly significant for quantum randomness generation, as it would remove the standard requirements for entanglement and multi-particle Bell tests while still providing device-independent guarantees against unbounded adversaries. However, the approach as described appears to rest on an assumption that single-system statistics alone can bound adversarial knowledge in a manner equivalent to non-local correlations.

major comments (2)

[Abstract] Abstract: the claim that measurements on single-particle states suffice for black-box certification is not supported by the protocol. Device-independent certification against deterministic adversaries requires violation of a Bell inequality, which in turn requires at least two subsystems and entanglement to produce non-local correlations; a single-particle black-box admits no such test, allowing a deterministic strategy to reproduce any output distribution exactly.
[Protocol] Protocol section (as described in the abstract and introduction): without an initial random seed, the measurement choices are fixed or deterministic, so no statistical test on the single-system outcomes can exclude a pre-programmed deterministic adversary while still accepting valid quantum data. This undermines the 'genuine' and 'black-box' certification claim.

minor comments (1)

[Introduction] Introduction: the distinction between the proposed 'black-box' notion and standard device-independent definitions should be made explicit, including any additional assumptions on the single-particle source or measurement apparatus.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive report. We address the major comments point by point below, indicating where revisions will be made to clarify the scope of our claims.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that measurements on single-particle states suffice for black-box certification is not supported by the protocol. Device-independent certification against deterministic adversaries requires violation of a Bell inequality, which in turn requires at least two subsystems and entanglement to produce non-local correlations; a single-particle black-box admits no such test, allowing a deterministic strategy to reproduce any output distribution exactly.

Authors: We agree that fully device-independent certification against an unbounded deterministic adversary requires Bell nonlocality and thus multiple subsystems. Our protocol achieves certification of randomness from single-particle measurements by verifying consistency with quantum statistics that cannot be reproduced by a classical deterministic model without access to the quantum state itself. We will revise the abstract to explicitly state that the result is a black-box certification for single-system quantum devices (semi-device-independent in nature) rather than a fully device-independent protocol relying on non-local correlations. revision: yes
Referee: [Protocol] Protocol section (as described in the abstract and introduction): without an initial random seed, the measurement choices are fixed or deterministic, so no statistical test on the single-system outcomes can exclude a pre-programmed deterministic adversary while still accepting valid quantum data. This undermines the 'genuine' and 'black-box' certification claim.

Authors: The absence of a random seed means measurement settings are fixed, limiting the ability to rule out all pre-programmed deterministic strategies. Our certification test instead relies on the observed output distribution matching the quantum prediction (e.g., via frequency or higher-moment checks) while bounding the adversary's predictive power under the assumption that the device implements the claimed single-particle quantum measurement. We will expand the protocol section with a formal security analysis showing the conditions under which a deterministic adversary fails the test, and we will qualify the 'genuine black-box' terminology accordingly. revision: partial

standing simulated objections not resolved

The fundamental limitation that single-system statistics cannot provide certification equivalent to Bell nonlocality against an unbounded deterministic adversary who controls the device.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external quantum principles

full rationale

The abstract and available claims present a demonstration of black-box randomness certification via single-particle measurements without seed or device assumptions. No equations, self-citations, or fitted parameters are shown that reduce the central result to its inputs by construction. The load-bearing premise invokes intrinsic quantum randomness and black-box certification bounds, which are independent of the paper's own data or definitions rather than self-referential. This matches the default expectation of non-circularity for papers whose core claim rests on established quantum features rather than renaming or fitting.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides insufficient detail to enumerate free parameters, axioms, or invented entities; the ledger is therefore empty.

pith-pipeline@v0.9.0 · 5394 in / 994 out tokens · 38630 ms · 2026-05-15T19:01:15.470908+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel (J uniqueness) unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 1 (No-measurement bound for antipodal phase estimation): without measurement mse=1/2; with measurement mse=1/4 (Theorem 2). Single non-separable |theta> as single-use random box.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking (D=3 forcing) unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Uses single-particle states and Born rule p[psi][x] = <psi|X_x^dagger X_x |psi>; no entanglement or initial seed required.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

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[1] [1]

URLhttps://doi

Pironio, S.et al.Random numbers certified by bell’s theorem.Nature464, 1021–1024 (2010). URLhttps://doi. org/10.1038/nature09008

work page doi:10.1038/nature09008 2010

[2] [2]

Certified randomness in quantum physics

Ac´ ın, A. & Masanes, L. Certified randomness in quantum physics.Nature540, 213–219 (2016). URLhttps: //doi.org/10.1038/nature20119

work page doi:10.1038/nature20119 2016

[3] [3]

Jordan Berg, Shouvanik Chakrabarti, Florian J

Liu, M.et al.Certified randomness using a trapped-ion quantum processor.Nature1–6 (2025). URLhttps://doi. org/10.1038/s41586-025-08737-1

work page doi:10.1038/s41586-025-08737-1 2025

[4] [4]

& Vidick, T

Brakerski, Z., Christiano, P., Mahadev, U., Vazirani, U. & Vidick, T. A cryptographic test of quantumness and certifiable randomness from a single quantum device.Journal of the ACM (JACM)68, 1–47 (2021)

work page 2021

[5] [5]

& Vidick, T

Mahadev, U., Vazirani, U. & Vidick, T. Efficient certifiable randomness from a single quantum device.arXiv preprint arXiv:2204.11353(2022). URLhttps://doi.org/10.48550/arXiv.2204.11353

work page doi:10.48550/arxiv.2204.11353 2022

[6] [6]

& Hung, S.-H

Aaronson, S. & Hung, S.-H. Certified randomness from quantum supremacy. InProceedings of the 55th Annual ACM Symposium on Theory of Computing, 933–944 (2023)

work page 2023

[7] [7]

Hidden variables, joint probability, and the bell inequalities.Physical Review Letters48, 291–295 (1982)

Fine, A. Hidden variables, joint probability, and the bell inequalities.Physical Review Letters48, 291–295 (1982). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.48.291

work page doi:10.1103/physrevlett.48.291 1982

[8] [8]

Hensen , author H

Hensen, B.et al.Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres.Nature 526, 682–686 (2015). URLhttp://dx.doi.org/10.1038/nature15759. GENUINE CERTIFIABLE RANDOMNESS FROM A BLACK-BOX 13

work page doi:10.1038/nature15759 2015

[9] [9]

Projecting computational power (2018)

Adleman, L. Projecting computational power (2018). URLhttps://adleman.usc.edu/ projecting-computational-power/

work page 2018

[10] [10]

& Vidick, T

Vazirani, U. & Vidick, T. Certifiable quantum dice: or, true random number generation secure against quantum adversaries. InProceedings of the forty-fourth annual ACM symposium on Theory of computing, 61–76 (2012)

work page 2012

[11] [11]

Amer, O.et al.Applications of certified randomness.arXiv preprint arXiv:2503.19759(2025)

work page arXiv 2025

[12] [12]

Wootters, W. K. & Zurek, W. H. A single quantum cannot be cloned.Nature299, 802–803 (1982). URLhttps: //doi.org/10.1038/299802a0

work page doi:10.1038/299802a0 1982

[13] [13]

Barnett, S. M. & Pegg, D. T. On the hermitian optical phase operator.Journal of Modern Optics36, 7–19 (1989). URLhttps://doi.org/10.1080/09500348914550021

work page doi:10.1080/09500348914550021 1989

[14] [14]

& Popescu, S

Aharonov, Y., Massar, S. & Popescu, S. Measuring energy, estimating hamiltonians, and the time-energy uncertainty relation.Physical Review A66, 052107 (2002). URLhttps://link.aps.org/doi/10.1103/PhysRevA.66.052107

work page doi:10.1103/physreva.66.052107 2002

[15] [15]

& Wright, J

O’Donnell, R. & Wright, J. Efficient quantum tomography (2016). URLhttps://doi.org/10.1145/2897518. 2897544

work page doi:10.1145/2897518 2016

[16] [16]

Shadow tomography of quantum states (2018)

Aaronson, S. Shadow tomography of quantum states (2018). URLhttps://doi.org/10.1145/3188745.3188802

work page doi:10.1145/3188745.3188802 2018

[17] [17]

Helstrom, C. W. Minimum mean-squared error of estimates in quantum statistics.Physics Letters A25, 101–102 (1967). URLhttps://www.sciencedirect.com/science/article/pii/0375960167903660

work page arXiv 1967

[18] [18]

S.Probabilistic and Statistical Aspects of Quantum Theory(North-Holland Publishing Company, 1982)

Holevo, A. S.Probabilistic and Statistical Aspects of Quantum Theory(North-Holland Publishing Company, 1982)

work page 1982

[19] [19]

L., Caves, C

Braunstein, S. L., Caves, C. M. & Milburn, G. J. Generalized uncertainty relations: Theory, examples, and lorentz invariance.Annals of Physics247, 135–173 (1996). URLhttp://www.sciencedirect.com/science/article/pii/ S0003491696900408

work page 1996

[20] [20]

T., Caves, C

Boixo, S., Flammia, S. T., Caves, C. M. & Geremia, J. Generalized limits for single-parameter quantum estimation. Phys. Rev. Lett.98(2007). URLhttps://doi.org/10.1103/PhysRevLett.98.090401

work page doi:10.1103/physrevlett.98.090401 2007

[21] [21]

& Demkowicz-Dobrza´ nski, R

Jarzyna, M. & Demkowicz-Dobrza´ nski, R. True precision limits in quantum metrology.New Journal of Physics17, 013010 (2015)

work page 2015

[22] [22]

& Jordan, A

Pang, S. & Jordan, A. N. Optimal adaptive control for quantum metrology with time-dependent hamiltonians. Nature Communications8, 14695 (2017). URLhttp://dx.doi.org/10.1038/ncomms14695

work page doi:10.1038/ncomms14695 2017

[23] [23]

G´ orecki, W., Demkowicz-Dobrza´ nski, R., Wiseman, H. M. & Berry, D. W.π-corrected heisenberg limit.Physical Review Letters124, 030501 (2020). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.124.030501

work page doi:10.1103/physrevlett.124.030501 2020

[24] [24]

Cram´ er, H.Mathematical methods of statistics(Princeton University Press, Princeton, 1946)

work page 1946

[25] [25]

Jelezko, J

Jelezko, F. & Wrachtrup, J. Single defect centres in diamond: a review.Phys. Status Solidi203, 3207 (2006). URL http://dx.doi.org/10.1002/pssa.200671403

work page doi:10.1002/pssa.200671403 2006

[26] [26]

R.et al.Nanoscale magnetic sensing with an individual electronic spin in diamond.Nature455, 644–647 (2008)

Maze, J. R.et al.Nanoscale magnetic sensing with an individual electronic spin in diamond.Nature455, 644–647 (2008). URLhttps://doi.org/10.1038/nature07279

work page doi:10.1038/nature07279 2008

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