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

• URL: http://arxiv.org/abs/2608.21783v1
• Date: Sat, 22 Aug 2026 05:31:54 GMT
• Title: Reinventing the Single-pixel Imaging Paradigm via Quantum-Operator-Based Signal Processing
• Abstract summary: Single-pixel imaging suffers severely from the decoupled acquisition-reconstruction hierarchy.<n>We introduce a quantum-operator-based SPI theoretical framework driven by coherent signal processing.<n>This work establishes a universal theoretical blueprint for next-generation quantum-enhanced sensing.
• Score: 1.1055300973238178
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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