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arxiv: 2604.08057 · v1 · submitted 2026-04-09 · 🪐 quant-ph

Orthogonalised Self-Guided Quantum Tomography: Insights from Single-Pixel Imaging

Kiki Dekkers , Alice Ruget , Fazilah Nothlawala , Sabrina Henry , Stirling Scholes , Miles Padgett , Andrew Forbes , Isaac Nape
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Jonathan Leach
This is my paper

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification 🪐 quant-ph
keywords self-guided quantum tomographysingle-pixel imagingorthogonalised ghost imagingquantum state reconstructionfidelity improvementmeasurement optimisation
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The pith

Orthogonalised self-guided quantum tomography achieves higher fidelity by importing an orthogonalisation step from single-pixel imaging.

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

The paper defines self-guided imaging as the direct classical linear counterpart to self-guided quantum tomography and demonstrates that it is mathematically equivalent to single-pixel imaging. It then transfers the orthogonalisation procedure recently developed for ghost imaging in single-pixel imaging to create orthogonalised SGQT. This adaptation requires no new hardware or measurements yet produces faster convergence and higher final fidelity, confirmed by both numerical simulations and laboratory experiments. A reader would care because it shows how classical imaging advances can be reused to make quantum state reconstruction more efficient and practical.

Core claim

Self-guided imaging is mathematically equivalent to single-pixel imaging, which permits the orthogonalisation step from orthogonalised ghost imaging to be applied directly to self-guided quantum tomography, improving reconstruction accuracy with no added experimental overhead.

What carries the argument

Orthogonalised SGQT, formed by adding an orthogonalisation step to the measurement patterns of SGQT, adapted from the orthogonalisation used in single-pixel imaging to decorrelate successive measurements.

If this is right

  • Numerical fidelity rises from 95.2 percent to 99.17 percent.
  • Experimental fidelity rises from 92.1 percent to 95.3 percent.
  • The procedure adds no extra experimental overhead.
  • Routines from single-pixel imaging and self-guided quantum tomography can be interchanged to further optimise measurements.

Where Pith is reading between the lines

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

  • The same mapping might allow other single-pixel imaging advances, such as compressed sensing patterns, to be imported into quantum tomography.
  • If the equivalence extends to noisy or incomplete data regimes, orthogonalised SGQT could reduce the total number of measurements needed for a target fidelity.
  • Testing the method on higher-dimensional states or different quantum platforms would clarify how widely the performance gain holds.

Load-bearing premise

The mathematical equivalence between self-guided imaging and single-pixel imaging permits the orthogonalisation procedure to transfer directly without introducing quantum-specific errors or hidden overhead.

What would settle it

An experiment in which orthogonalised SGQT either fails to raise fidelity above standard SGQT or requires additional measurements beyond the standard protocol.

Figures

Figures reproduced from arXiv: 2604.08057 by Alice Ruget, Andrew Forbes, Fazilah Nothlawala, Isaac Nape, Jonathan Leach, Kiki Dekkers, Miles Padgett, Sabrina Henry, Stirling Scholes.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of gradient descent via conventional (grey [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of error for simulation of single-pixel [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of self-guided quantum tomography performance for the SGQT (solid blue) and OSGQT (dashed red). 2 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of self-guided quantum tomography, self-guided imaging and single-pixel imaging. We introduce self-guided [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of error for single-pixel imaging vs. self [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of output images for single-pixel imaging [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A 405 nm CW laser is focused into a ppKTP crystal to undergo type-I SPDC. The pump beam is blocked by a 550 nm [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of recorded counts for SGQT (solid blue) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison of the inferred infidelities of (a) SGQT [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. SGQT (solid blue) and OSGQT (dashed red) experimental performance for different scaling parameters [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Numerical and experimental comparison of SGQT and OGQT performance for difference noise levels. Unknown [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
read the original abstract

We introduce the concept of self-guided imaging (SGI) as a linear analogue of self-guided quantum tomography (SGQT). We show that SGI is mathematically equivalent to single-pixel imaging (SPI). Taking inspiration from orthogonalised ghost imaging, a recent advance in SPI, we introduce orthogonalised SGQT. This requires no additional experimental overhead and leads to faster and more accurate final convergence, as we demonstrate numerically (fidelity $95.2\% \rightarrow 99.17\%$) and experimentally (fidelity $92.1\% \rightarrow 95.3\%$). This work suggests that further routines from SPI and SGQT can be interchanged to optimise measurements and convergence.

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

0 major / 3 minor

Summary. The paper claims to introduce self-guided imaging (SGI) as a linear analogue of self-guided quantum tomography (SGQT), establish its mathematical equivalence to single-pixel imaging (SPI), and adapt orthogonalisation from ghost imaging to create orthogonalised SGQT. This new approach is said to require no additional experimental overhead while providing faster and more accurate convergence, as shown by numerical fidelity improvements from 95.2% to 99.17% and experimental improvements from 92.1% to 95.3%. It concludes by suggesting that further routines from SPI and SGQT can be interchanged for optimization.

Significance. This result, if the equivalence and transfer are rigorously established, is significant because it creates a direct link between quantum tomography techniques and classical single-pixel imaging methods. The explicit numerical and experimental demonstrations of fidelity gains without added overhead are particular strengths, offering reproducible evidence for the practical utility. Such cross-fertilization could accelerate the development of efficient quantum measurement protocols by leveraging mature techniques from the classical imaging community.

minor comments (3)
  1. The reported fidelity values lack accompanying statistical details such as standard deviations or the number of experimental trials, making it harder to gauge the robustness of the claimed improvements.
  2. A more detailed explanation of how the orthogonalisation procedure is implemented in the quantum setting, including any potential differences from the classical SPI case, would enhance clarity even if the equivalence is exact.
  3. The manuscript would benefit from a figure or table illustrating the convergence speed comparison between SGQT and orthogonalised SGQT to visually support the 'faster convergence' claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the contributions, and recommendation for minor revision. We are pleased that the significance of linking SGQT with classical SPI techniques is recognized.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines SGI as a linear analogue of SGQT, establishes its mathematical equivalence to SPI via direct proof, and transfers the orthogonalisation routine from prior orthogonalised ghost imaging work in SPI. Central performance claims (fidelity gains from 95.2% to 99.17% numerically and 92.1% to 95.3% experimentally) are supported by independent simulation and lab measurements rather than any derivation by construction. No self-definitional loops, fitted inputs presented as predictions, load-bearing self-citations reducing the result to unverified inputs, or ansatz smuggling appear in the derivation chain. The equivalence and transfer are self-contained with external empirical validation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the claimed equivalence and orthogonalisation step are stated without derivation details.

pith-pipeline@v0.9.0 · 5436 in / 1003 out tokens · 55605 ms · 2026-05-10T17:11:55.538043+00:00 · methodology

discussion (0)

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Reference graph

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