Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.08057

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, Jonathan Leach

quant-phSubmitted Apr 9, 2026• Announced Apr 10, 2026• 0 citations
arXivHTMLPDF

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.

Related papers

High-Dimensional Self-Guided Quantum Tomography of Laguerre-Gaussian Modes

Ruomin Bi, Dawei Lyu, Qianlei Liu +3 more

We experimentally demonstrate self-guided quantum tomography (SGQT) for states encoded by Laguerre-Gaussian (LG) modes. By iteratively learning the unknown quantum states from adaptively optimized projection measurements, we experimentally achieve a reconstruction fidelity of more than 97.3% in eight-dimensional systems.

•Jan 1, 2026•0 citations

Reinventing the Single-pixel Imaging Paradigm via Quantum-Operator-Based Signal Processing

Bu-Ran Yu, Yi-Zhu Zhang, Kan-Xu Jia +3 more

A fundamental bottleneck across modern computational imaging and high-dimensional sensing is the conventional decoupled acquisition-reconstruction hierarchy, which subjects high-dimensional spatial sensing to the classical shot-noise limit and intense computational overhead. As a prominent manifestation of this limitation, single-pixel imaging (SPI) suffers severely from this paradigm. We reinvent this paradigm by introducing a quantum-operator-based SPI theoretical framework driven by coherent signal processing. Within this architecture, the spatial inverse problem is analytically mapped into the eigenvalue spectrum of a quantum operator via tailored light-matter interactions. By analytically synthesizing non-linear reconstruction operators via ultra-shallow quantum architectures, we theoretically demonstrate an exponential decay of spatial approximation errors, completely bypassing traditional linear solvers. This operator-space embedding not only shields reconstruction from noise via a strategic error-saturation zone but also bridges the gap from classical shot-noise scaling $\mathcal{O}(1/\sqrt{N_{\text{ph}}})$ to the ultimate Heisenberg limit $\mathcal{O}(1/N_{\text{ph}})$. Crucially, while formulated within SPI, this coherent operator paradigm fundamentally extends to general photon-starved, high-dimensional imaging modalities. This work establishes a universal theoretical blueprint for next-generation quantum-enhanced sensing, shifting the paradigm from iterative optimization to coherent operator-space evolution.

quant-pharXiv:2608.21783•Aug 25, 2026•0 citations

Self-Guided Quantum Tomography

Christopher Ferrie

We introduce a self-learning tomographic technique in which the experiment guides itself to an estimate of its own state. Self-guided quantum tomography uses measurements to directly test hypotheses in an iterative algorithm which converges to the true state. We demonstrate through simulation on many qubits that Self-guided quantum tomography is a more efficient and robust alternative to the usual paradigm of taking a large amount of informationally complete data and solving the inverse problem of postprocessed state estimation.

arXiv:1406.4101•Physical Review Letters•Nov 7, 2014•124 citations

Practical adaptive quantum tomography

Christopher Granade, Christopher Ferrie, Steven T. Flammia

We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods.Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states.By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques.We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.Quantum information processing (QIP) promises advantages in a wide range of different contexts, including machine learning [2-4], chemistry simulation [5][6][7], and number theory [8,9].As such, the experimental effort to build useful QIP devices has exploded in recent years.In the course of this effort, quantum tomography is a valuable tool for diagnosing and debugging small quantum devices, and has subsequently seen a variety of different advances.In particular, Bayesian approaches to tomography which are especially well suited to utilizing prior information and adapting to changing experimental conditions have developed significantly in recent years [10-13], presenting a useful experimental tool [14][15][16].In this paper we demonstrate the efficiency and accuracy of an adaptive tomography protocol that we call PAQT: practical adaptive quantum tomography.PAQT intelligently selects new measurements based on the outcomes of previous ones [10,[17][18][19][20][21].Adaptivity has been experimentally demonstrated [14,15,[22][23][24][25], but is not currently standard practice.Though adaptivity increases accuracy, the computational costs incurred outweigh that of simply repeating standard measurements many times.The PAQT approach employs a simple heuristic that can be efficiently computed between measurements, even with embedded hardware [26][27][28][29].The algorithm we propose is therefore compatible with modern experimental design and avoids an important limitation of previous approaches.We base our algorithm off of self-guided quantum tomography (SGQT), which treats adaptive tomography as a direct optimization problem rather than a new optimization problem between each measurement [30].Though this affords an efficient and easy to implement adaptive heuristic, SGQT is not without its limitations.It requires assuming that the target state is pure, and it does not return rich region estimates for a state.What PAQT achieves is to effectively combine SGQT with conventional and easily-implemented tomographic estimators, such as the Bayesian particle filter or least-squares fit (LSF) estimators.Under this approach, an experimentalist can collect data using SGQT (even if its assumptions are not met), and then post-process this data using particle filtering or LSF.The benefit of PAQT is two-fold.(1) From the point of view of traditional tomography, it gives an adaptive tomography protocol requiring only modest computational resources, as the bulk of the computational cost is offloaded to post-processing.(2) From the point of view of simulation-based optimization tomography (such as SGQT), it effectively augments the output with region estimation providing a statistically robust quantification of uncertainty.Thus, while we do not explicitly demonstrate that the improved scaling of Ferrie [30] remains in the more general case considered here, PAQT does provide a practical and efficient procedure for performing adaptive quantum tomography with rigorous statistical principles.

arXiv:1605.05039•New Journal of Physics•Sep 29, 2017•51 citations

Quantum Ghost Imaging by Sparse Spatial Mode Reconstruction

Fazilah Nothlawala, Chané Moodley, Neelan Gounden +2 more

Abstract In a conventional quantum imaging experiment, the image of the object is retrieved directly with single photon camera technology, or computationally with a single‐pixel detector and pixelated projective masks. In all these approaches, the resolution of the image is dictated by the pixel resolution of the detection devices. In this paper, the traditional spatial basis of pixels is replaced with spatial modes, exploiting their unique features to enhance image fidelity and resolution and improve reconstruction accuracy through modal sparsity. This approach can be used even when the modes are not orthogonal, demonstrating the principle with highly efficient phase‐only approximations to the modal basis. By numerical simulation and experimental analysis, the advantages of this approach are illustrated, which include faster convergence to the object, with higher signals and fidelity, which are demonstrated with an order of magnitude less masks than conventional approaches for the same fidelity in outcome. Unlike the basis of pixels, the resolution of the image is not dictated by the resolution of the detectors, opening a path to high‐resolution quantum imaging of complex objects.

Advanced Quantum Technologies•Jan 6, 2025•7 citations

Quantum ghost imaging with a modal basis

Fazilah Nothlawala, Chané Moodley, Neelan Gounden +2 more

Quantum ghost imaging harnesses entangled photon pairs to form images using light that never directly interacts with the object. Conventional approaches rely on pixelated detectors or spatial masks, where the resolution is fundamentally limited by the pixel size and thus bounded by the Rayleigh criterion. In this work, we present a modal approach that replaces pixel-based detection with measurements in a basis of structured modes. By reconstructing images through tailored spatial modes, we decouple resolution from the physical limitations of detectors and instead tie it to the system’s optical precision and computational control. We demonstrate that even non-orthogonal modal sets can achieve high fidelity image reconstruction by exploiting modal sparsity, significantly reducing the number of required measurements. Using phase-only approximations of Hermite-Gaussian modes, we avoid the loss associated with complex amplitude modulation while retaining high reconstruction fidelity. The result is a high-resolution, high-efficiency quantum ghost imaging technique powered by structured light, opening new possibilities for photon-efficient imaging in low-light and quantum-limited regimes, such as biological microscopy and remote sensing.

Optical and Quantum Sensing and Precision Metrology II•Mar 5, 2026•0 citations
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%→99.17%95.2\% \rightarrow 99.17\%95.2%→99.17%) and experimentally (fidelity 92.1%→95.3%92.1\% \rightarrow 95.3\%92.1%→95.3%). This work suggests that further routines from SPI and SGQT can be interchanged to optimise measurements and convergence.
A fundamental bottleneck across modern computational imaging and high-dimensional sensing is the conventional decoupled acquisition-reconstruction hierarchy, which subjects high-dimensional spatial sensing to the classical shot-noise limit and intense computational overhead. As a prominent manifestation of this limitation, single-pixel imaging (SPI) suffers severely from this paradigm. We reinvent this paradigm by introducing a quantum-operator-based SPI theoretical framework driven by coherent signal processing. Within this architecture, the spatial inverse problem is analytically mapped into the eigenvalue spectrum of a quantum operator via tailored light-matter interactions. By analytically synthesizing non-linear reconstruction operators via ultra-shallow quantum architectures, we theoretically demonstrate an exponential decay of spatial approximation errors, completely bypassing traditional linear solvers. This operator-space embedding not only shields reconstruction from noise via a strategic error-saturation zone but also bridges the gap from classical shot-noise scaling O(1/Nph)\mathcal{O}(1/\sqrt{N_{\text{ph}}})O(1/Nph​​) to the ultimate Heisenberg limit O(1/Nph)\mathcal{O}(1/N_{\text{ph}})O(1/Nph​). Crucially, while formulated within SPI, this coherent operator paradigm fundamentally extends to general photon-starved, high-dimensional imaging modalities. This work establishes a universal theoretical blueprint for next-generation quantum-enhanced sensing, shifting the paradigm from iterative optimization to coherent operator-space evolution.
We introduce a self-learning tomographic technique in which the experiment guides itself to an estimate of its own state. Self-guided quantum tomography uses measurements to directly test hypotheses in an iterative algorithm which converges to the true state. We demonstrate through simulation on many qubits that Self-guided quantum tomography is a more efficient and robust alternative to the usual paradigm of taking a large amount of informationally complete data and solving the inverse problem of postprocessed state estimation.
We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods.Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states.By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques.We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.Quantum information processing (QIP) promises advantages in a wide range of different contexts, including machine learning [2-4], chemistry simulation [5][6][7], and number theory [8,9].As such, the experimental effort to build useful QIP devices has exploded in recent years.In the course of this effort, quantum tomography is a valuable tool for diagnosing and debugging small quantum devices, and has subsequently seen a variety of different advances.In particular, Bayesian approaches to tomography which are especially well suited to utilizing prior information and adapting to changing experimental conditions have developed significantly in recent years [10-13], presenting a useful experimental tool [14][15][16].In this paper we demonstrate the efficiency and accuracy of an adaptive tomography protocol that we call PAQT: practical adaptive quantum tomography.PAQT intelligently selects new measurements based on the outcomes of previous ones [10,[17][18][19][20][21].Adaptivity has been experimentally demonstrated [14,15,[22][23][24][25], but is not currently standard practice.Though adaptivity increases accuracy, the computational costs incurred outweigh that of simply repeating standard measurements many times.The PAQT approach employs a simple heuristic that can be efficiently computed between measurements, even with embedded hardware [26][27][28][29].The algorithm we propose is therefore compatible with modern experimental design and avoids an important limitation of previous approaches.We base our algorithm off of self-guided quantum tomography (SGQT), which treats adaptive tomography as a direct optimization problem rather than a new optimization problem between each measurement [30].Though this affords an efficient and easy to implement adaptive heuristic, SGQT is not without its limitations.It requires assuming that the target state is pure, and it does not return rich region estimates for a state.What PAQT achieves is to effectively combine SGQT with conventional and easily-implemented tomographic estimators, such as the Bayesian particle filter or least-squares fit (LSF) estimators.Under this approach, an experimentalist can collect data using SGQT (even if its assumptions are not met), and then post-process this data using particle filtering or LSF.The benefit of PAQT is two-fold.(1) From the point of view of traditional tomography, it gives an adaptive tomography protocol requiring only modest computational resources, as the bulk of the computational cost is offloaded to post-processing.(2) From the point of view of simulation-based optimization tomography (such as SGQT), it effectively augments the output with region estimation providing a statistically robust quantification of uncertainty.Thus, while we do not explicitly demonstrate that the improved scaling of Ferrie [30] remains in the more general case considered here, PAQT does provide a practical and efficient procedure for performing adaptive quantum tomography with rigorous statistical principles.
Abstract In a conventional quantum imaging experiment, the image of the object is retrieved directly with single photon camera technology, or computationally with a single‐pixel detector and pixelated projective masks. In all these approaches, the resolution of the image is dictated by the pixel resolution of the detection devices. In this paper, the traditional spatial basis of pixels is replaced with spatial modes, exploiting their unique features to enhance image fidelity and resolution and improve reconstruction accuracy through modal sparsity. This approach can be used even when the modes are not orthogonal, demonstrating the principle with highly efficient phase‐only approximations to the modal basis. By numerical simulation and experimental analysis, the advantages of this approach are illustrated, which include faster convergence to the object, with higher signals and fidelity, which are demonstrated with an order of magnitude less masks than conventional approaches for the same fidelity in outcome. Unlike the basis of pixels, the resolution of the image is not dictated by the resolution of the detectors, opening a path to high‐resolution quantum imaging of complex objects.
Quantum ghost imaging harnesses entangled photon pairs to form images using light that never directly interacts with the object. Conventional approaches rely on pixelated detectors or spatial masks, where the resolution is fundamentally limited by the pixel size and thus bounded by the Rayleigh criterion. In this work, we present a modal approach that replaces pixel-based detection with measurements in a basis of structured modes. By reconstructing images through tailored spatial modes, we decouple resolution from the physical limitations of detectors and instead tie it to the system’s optical precision and computational control. We demonstrate that even non-orthogonal modal sets can achieve high fidelity image reconstruction by exploiting modal sparsity, significantly reducing the number of required measurements. Using phase-only approximations of Hermite-Gaussian modes, we avoid the loss associated with complex amplitude modulation while retaining high reconstruction fidelity. The result is a high-resolution, high-efficiency quantum ghost imaging technique powered by structured light, opening new possibilities for photon-efficient imaging in low-light and quantum-limited regimes, such as biological microscopy and remote sensing.