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arXiv:2608.21783

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

Bu-Ran Yu, Yi-Zhu Zhang, Kan-Xu Jia, Qian-Qian Bao, Shao-Ying Meng, Xi-Hao Chen

quant-phphysics.opticsSubmitted Aug 22, 2026• Announced Aug 25, 2026• 0 citations
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Abstract

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.

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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.
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.
Quantum sensing can enhance imaging performance by reducing measurement noise below the classical limit, thereby improving the signal-to-noise ratio (SNR) of acquired data. In conventional quantum imaging schemes, squeezing is applied independently to each pixel or spatial mode, leading to a quantum resource cost that scales linearly with image dimension. This approach implicitly separates quantum enhancement from classical post-processing, treating them as independent layers. In this work, we demonstrate that integrating quantum resource allocation with the guidance from classical compressive imaging, via co-design between the quantum hardware layer and the classical software layer, substantially reduces the required quantum resources. We employ principal component analysis (PCA) to identify a low-dimensional principal component subspace for measurement and apply squeezing selectively to the most informative spatial modes corresponding to these principal components. Our numerical experiments show that high-accuracy image classification and high-fidelity image reconstruction can be achieved with significantly fewer squeezed modes compared to pixel-wise squeezing. Our results establish a joint quantum classical co-design framework for resource-efficient quantum-enhanced imaging.
How many measurements are fundamentally required to capture a signal. Shannon's information theory established the bedrock of this question in 1948, the Nyquist Shannon theorem set the first answer, and compressed sensing (CS) rewrote it in 2006 by reducing the required measurement number to M = O(Klog(N/K)) for a K sparse signal. Here, we propose quantum compressed sensing (QCS), a paradigm that reframes signal acquisition as a unitary quantum evolution. By encoding high dimensional signal information into a single quantum probe state, then introducing domain-alignment evolution,a physically realizable unitary transformation that maps the sparse basis directly onto the measurement basis. QCS executes the support-set search at the quantum level without consuming measurement trials. The logarithmic penalty vanishes, compressing the required measurement number from the classical bound to M =O(K) and reducing reconstruction from ill posed optimization to linear estimation. We experimentally validate QCS using frequency and time domain sparse signals, confirming that the measurement number scales linearly with sparsity and decouples entirely from the signal dimension. Our work provides a physical pathway toward ultimate information acquisition efficiency, with broad implications for sensing, imaging, and communication.
Entangled quantum probes can achieve Heisenberg-limited measurement precision, but this advantage is typically destroyed by noise. We address this issue by introducing a framework that we call encoded quantum signal processing, which unifies quantum error detection and quantum signal processing into an effective single-qubit framework, and provides a paradigm for constructing logical sensors that are robust to noise while remaining sensitive to the signal of interest. We show that encoding sensor qubits into a repetition code and using syndrome measurements as a signal-processing primitive restores Heisenberg scaling under realistic noise, without applying recovery operations. We prove that product-state sensing with syndrome post-processing is fundamentally limited to standard quantum limit (SQL) scaling, and develop four protocols that overcome this barrier through entanglement or sequential signal amplification, achieving Heisenberg-limited precision with exponential error suppression in code distance. For spatially inhomogeneous fields, Bayesian marginalization preserves Heisenberg scaling provided noise decreases sufficiently with system size. The underlying mechanism, which we formalize as encoded quantum signal processing, reduces multi-qubit metrology to an effective single-qubit problem where syndrome measurement implements nonlinear signal transformations. Numerical simulations validate the theoretical predictions: syndrome-based inference achieves near-Heisenberg scaling at noise levels where bare probes approach the SQL, and a concatenated protocol maintains this scaling under joint transverse noise and longitudinal inhomogeneities.
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 sensing offers sensitivities surpassing classical limits, yet practical deployment is often constrained by noise and inefficient signal extraction. This systematic review synthesizes literature from 2015 to 2025 and maps the landscape of data-driven signal processing across diverse platforms, including nitrogen-vacancy (NV) centers and cold atom interferometers. Emerging methodologies are categorized and emphasis is placed on the dominance of hybrid quantum-classical architectures where classical machine learning manages high-dimensional data processing while quantum processors execute specific primitives like feature mapping. Our findings demonstrate that advanced statistical frameworks such as Variational Bayesian Inference (VBI) enable scalable multi-parameter estimation with polynomial complexity, allowing dozens of sensor parameters to be estimated within minutes. Meanwhile, quantum sensing missions in GPS-denied navigation have achieved operational gains through AI-automated software designed to manage quantum hardware drifts and environmental noise, despite a persistent reality gap for generalized quantum machine learning. We further analyze the critical sensitivity-robustness dilemma inherent in entangled sensors and discuss mitigation strategies such as covariant quantum error-correcting codes. We also distinguish between theoretical Quantum Fisher Information (QFI) and realized Mean Squared Error (MSE) of sensor outputs to resolve benchmarking inconsistencies in quantum metrology, and propose a "Gold Standard" reproducibility framework tailored for the Noisy Intermediate-Scale Quantum (NISQ) era to promote automated workflows and hardware calibration transparency. This review provides a strategic roadmap for researchers to bridge the gap between theoretical sensitivity and reliable, software-defined operational utility in quantum sensing.