AI 中文总结
本研究针对单像素成像的传统瓶颈，提出基于量子算子的相干信号处理框架，突破散粒噪声极限，为量子增强传感提供通用理论蓝图。
AI 中文摘要
现代计算成像与高维传感领域存在一个核心瓶颈：传统的采集-重建分离层级，使高维空间传感受限于经典散粒噪声极限且计算开销巨大，单像素成像（SPI）便是该局限的典型体现。本研究引入基于量子算子的SPI理论框架，由相干信号处理驱动，将空间逆问题通过定制的光-物质相互作用解析映射为量子算子的本征值谱；通过超浅量子架构解析合成非线性重建算子，从理论上证明空间近似误差呈指数衰减，完全绕过传统线性求解器。该算子空间嵌入不仅通过策略性误差饱和区使重建免受噪声影响，还将经典散粒噪声缩放$\boldsymbol{\text{O}}(1/\boldsymbol{\text{N}}_{\text{ph}})$突破至终极海森堡极限$\boldsymbol{\text{O}}(1/\boldsymbol{\text{N}}_{\text{ph}})$。关键在于，该相干算子范式虽以SPI为基础构建，却可从根本上扩展至光子匮乏型高维成像模态，为下一代量子增强传感确立了通用理论蓝图，将范式从迭代优化转向相干算子空间演化。
英文摘要
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.
