arxiv: 2604.12724 · v1 · submitted 2026-04-14 · 🪐 quant-ph

Recognition: unknown

Testing the 3D QRNG by Undoing

J.M. Ag\"uero Trejo , Cristian S. Calude , O.C. Stoica

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Pith reviewed 2026-05-10 14:53 UTC · model grok-4.3

classification 🪐 quant-ph

keywords 3D QRNGquantum random number generatorunitary evolutionincomputabilityunpredictabilityphotonic deviceerror verificationquantum certification

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The pith

Undoing the unitary evolution tests whether a photonic 3D quantum random number generator produces strongly unpredictable sequences.

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

The paper proposes a method to test a photonic 3D QRNG by reversing the unitary evolution the device performs on its input. This reversal checks whether the generator matches its theoretical design by confirming unitarity, measuring noise levels, and spotting issues such as photon loss or fabrication errors. If the reversal recovers the expected initial state within noise bounds, the output sequences exhibit the strong incomputability and unpredictability claimed by the underlying theory. The same procedure also avoids interference from quantum measurement accuracy limits. The test can be embedded directly in the generator to provide built-in certification.

Core claim

By undoing the unitary evolution realized by the 3D QRNG, the test verifies the unitarity of the process, the magnitude of the noise, photon loss, and systematic fabrication errors. This confirmation establishes the strong incomputability and unpredictability of the generated random sequences or indicates the corrections required if deviations are found. The approach ensures the QRNG is not constrained by the limits of quantum measurement accuracy described in the Wigner-Araki-Yanase Theorem.

What carries the argument

Undoing the unitary evolution, which reverses the quantum transformation to expose any deviations from ideal unitarity or unexpected errors.

If this is right

The test verifies unitarity and the magnitude of noise in the 3D QRNG.
It detects errors such as photon loss or systematic fabrication issues.
It confirms the strong incomputability and unpredictability of the output sequences.
It shows how to correct the device if necessary.
The QRNG avoids problems arising from quantum measurement accuracy limits.

Where Pith is reading between the lines

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

Integration of the test into the device could enable ongoing self-certification during normal operation.
The reversal technique offers a direct experimental check on theoretical randomness properties that are otherwise hard to observe.

Load-bearing premise

The unitary evolution performed by the 3D QRNG can be experimentally undone accurately enough to detect all relevant errors without the reversal introducing uncorrectable new distortions.

What would settle it

If performing the undoing operation on the output state fails to recover the initial state within the bounds set by the expected noise level, this would indicate that the QRNG does not operate according to the underlying theory or that the test itself is flawed.

Figures

Figures reproduced from arXiv: 2604.12724 by Cristian S. Calude, J.M. Ag\"uero Trejo, O.C. Stoica.

**Figure 1.** Figure 1: Reproduced from [7]. Physical realization of the universal unitary decomposition Ux by means of three-mode multiport interferometer. An arrangement of Mach–Zehnder interferometers consisting of phase shifters and balanced directional couplers illustrates its construction. Here, η = acos √ 2 3 . 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: Imprecise 3D-QRNG. The effect of using MMIs is that we have additional phase shifts, which contribute as additional phase shift matrices in equation (11). 7 Testing unitarity by undoing the QRNG The test aims to verify 1. the unitarity of the realized QRNG, and 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Phase shift gate. To test this by reconstructing the original state, we add another phase shift gate with opposite phase, as in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** Figure 5: Testing the 3D-QRNG by undoing. At the outputs of the 3D-QRNG implementing the transformation Uex, we connect the inputs of a mirrored version, which implements the inverse transformation Ue† x, and verify that we recover the input state. The test is successful if the output of the mirror QRNG is identical to the inputs of the original QRNG. In this case, the input is fully reconstructed and will show that… view at source ↗

**Figure 6.** Figure 6: Undoing the unitary transformation Uex. A way to test that UexUe† x = I, verifying the unitarity of the transformation Uex, is to compare the output after the inversion with the input by using interference. More precisely, use a beam splitter to split a photon into two equal-amplitude components, pass a component through the implementation of UexUe† x and then make it interfere with the other component, en… view at source ↗

read the original abstract

We propose a method to test whether a photonic 3D QRNG works according to the underlying theory, thereby generating highly incomputable/unpredictable sequences of random digits. The test relies on undoing the unitary evolution realized by the 3D QRNG. The test verifies the unitarity, the magnitude of the noise, and other potential errors, such as photon loss or systematic and reproducible fabrication errors. Therefore, the test can confirm the theoretically proven features of the 3D QRNG, such as strong incomputability and unpredictability, or how one has to correct it, if necessary. In addition, the test ensures that the QRNG is not affected by limits of quantum measurement accuracy, as those described in the Wigner-Araki-Yanase Theorem. The test can be easily incorporated into the QRNG and used as a means of experimental certification.

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 sketches a test for 3D QRNGs by reversing their unitary evolution to check unitarity and noise, but offers no derivations or data to show it works.

read the letter

The core idea is to certify a photonic 3D QRNG by undoing the unitary evolution it applies, then using the outcome to bound deviations from ideal behavior, measure noise, and flag photon loss or fabrication errors. If the reversal succeeds, the test is supposed to confirm that the device meets the conditions for the earlier theoretical proof of strong incomputability in its output bits, or else show what corrections are needed. It also claims to sidestep limits from the Wigner-Araki-Yanase theorem on measurement precision. That reversal step is the main new element presented here. It is a direct, optics-friendly way to turn the theoretical assumptions into something an experimenter could in principle check on the hardware itself. The approach avoids circularity by treating the reversal as an independent experimental probe rather than deriving the desired properties from fitted parameters. On the positive side, it connects cleanly to existing work on QRNG certification and gives a concrete handle on the practical conditions that the incomputability proofs require. The suggestion that the test can be built into the device itself is also practical. The main limitation is that the description stays at the level of an outline. There are no equations showing how the reversed state quantifies the error bounds, no analysis of how much precision the reversal itself needs, and no simulation or experimental data demonstrating that the method actually detects the claimed errors without introducing new ones. Implementing an accurate undo in a real photonic setup will face its own noise and alignment issues, and it is not yet clear whether those can be controlled tightly enough to certify the incomputability properties at the level claimed. This is aimed at people working on quantum random number generators and device verification in quantum optics. A reader already familiar with the 3D QRNG theory would see a useful next step for turning proofs into testable hardware, but would still need the missing technical details before trying to use it. The paper deserves peer review. The idea is straightforward enough that referees can ask for the required derivations and feasibility checks without starting from zero.

Referee Report

3 major / 0 minor

Summary. The manuscript proposes a certification test for a photonic 3D quantum random number generator (QRNG) that involves undoing the unitary evolution implemented by the device. This is claimed to verify the unitarity of the evolution, quantify the magnitude of noise, detect errors such as photon loss or systematic fabrication errors, and thereby confirm the strong incomputability and unpredictability of the generated random sequences as per prior theoretical results, or indicate necessary corrections. Additionally, the test is said to ensure the QRNG is unaffected by quantum measurement accuracy limits from the Wigner-Araki-Yanase Theorem and can be easily incorporated for experimental certification.

Significance. If the proposed undoing procedure can be realized experimentally with sufficient precision, it would offer a valuable self-certification mechanism for QRNGs, directly linking experimental performance to the theoretical conditions required for high-quality randomness generation. This could enhance trust in QRNG devices for applications requiring provable unpredictability. However, the current manuscript is a conceptual outline without any derivations, specific protocols, error bounds, or simulation results, so its significance remains potential rather than demonstrated.

major comments (3)

The central claim that 'undoing the unitary evolution' verifies unitarity and noise magnitude is not supported by any derivation, measurement scheme, or error analysis in the manuscript. No specific method is described for implementing the inverse unitary or for quantifying deviations from ideal behavior.
The statement that the test 'ensures that the QRNG is not affected by limits of quantum measurement accuracy, as those described in the Wigner-Araki-Yanase Theorem' lacks any explanation or argument showing how the undoing process circumvents or mitigates these limitations.
The proposal assumes that the reversal can be performed without introducing uncorrectable distortions or requiring unattainable precision, but no analysis of experimental feasibility, precision requirements, or potential new error sources from the undoing step is provided, which is load-bearing for the certification claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below, providing clarifications based on the conceptual nature of the proposal while indicating where the manuscript will be revised for greater rigor.

read point-by-point responses

Referee: The central claim that 'undoing the unitary evolution' verifies unitarity and noise magnitude is not supported by any derivation, measurement scheme, or error analysis in the manuscript. No specific method is described for implementing the inverse unitary or for quantifying deviations from ideal behavior.

Authors: The manuscript presents a high-level conceptual outline rather than a fully derived protocol. The inverse unitary is implemented by reversing the sequence of photonic operations (e.g., conjugate phases on beam splitters and phase shifters in the 3D interferometer). Deviations are quantified by comparing the measured output state after undoing to the known initial state via fidelity or by checking that the output statistics match the expected uniform distribution within noise bounds. We will add a new subsection with a schematic diagram of the test setup and basic error analysis using standard quantum optics fidelity measures. revision: yes
Referee: The statement that the test 'ensures that the QRNG is not affected by limits of quantum measurement accuracy, as those described in the Wigner-Araki-Yanase Theorem' lacks any explanation or argument showing how the undoing process circumvents or mitigates these limitations.

Authors: The Wigner-Araki-Yanase theorem limits precise measurement of observables non-commuting with conserved quantities. Our test mitigates this by verifying global reversibility of the evolution back to the initial single-photon state rather than performing direct high-accuracy measurements on the generated bits during operation. Successful undoing with high fidelity confirms unitarity without requiring precise readout of non-commuting observables in the randomness extraction step. We will insert a concise explanatory paragraph with a reference to the theorem in the revised manuscript. revision: yes
Referee: The proposal assumes that the reversal can be performed without introducing uncorrectable distortions or requiring unattainable precision, but no analysis of experimental feasibility, precision requirements, or potential new error sources from the undoing step is provided, which is load-bearing for the certification claim.

Authors: We agree that experimental feasibility requires explicit discussion. In photonic 3D QRNGs the inverse can be realized with comparable precision to the forward unitary using the same integrated-optic components; additional losses or phase errors introduced by the undoing stage are measurable and can be calibrated out when quantifying total noise. We will add a paragraph on current-technology precision requirements (e.g., phase stability of ~0.01 rad) and how new errors are folded into the existing noise budget. A full numerical simulation lies beyond the scope of this conceptual paper but will be noted as future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper proposes an experimental certification procedure that reverses the 3D QRNG unitary evolution to verify unitarity, bound noise and errors (including photon loss and fabrication issues), and thereby confirm or correct the conditions under which prior theoretical results on strong incomputability hold. No load-bearing step in the described method reduces by construction to a self-definition, a fitted parameter renamed as a prediction, or a self-citation chain that renders the central claim tautological. The test is framed as an independent experimental check whose validity rests on the feasibility of the reversal operation rather than on re-deriving the incomputability properties from the test itself. Minor self-citation of the underlying theory is present but not load-bearing for the test procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proposal rests on standard quantum mechanics assumptions about unitary evolution and the applicability of the Wigner-Araki-Yanase theorem to the device, with no free parameters, new entities, or ad-hoc postulates introduced in the abstract.

axioms (2)

domain assumption The 3D QRNG realizes a unitary evolution that can be experimentally undone
The test method depends on the ability to reverse the device's quantum process to verify its properties.
domain assumption Quantum measurement limits described by the Wigner-Araki-Yanase theorem apply to the QRNG and can be addressed by the test
The abstract states the test ensures the QRNG is not affected by these limits.

pith-pipeline@v0.9.0 · 5450 in / 1480 out tokens · 54193 ms · 2026-05-10T14:53:53.064348+00:00 · methodology

discussion (0)

Reference graph

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