SSP-QST：用于光子量子态层析成像的谱子空间纯化
SSP-QST: Spectral Subspace Purification for Photonic Quantum State Tomography
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中文总结 AI 辅助
研究针对光子量子传感中实际量子态层析成像的本征值污染问题，提出谱子空间纯化方法SSP-QST，它是秩自适应后处理层，无需秩先验等，模拟中实现高保真度并提高测量效率，为量子传感提供可靠轻量级重建方法。
中文摘要 AI 辅助
光子量子传感常使用低秩纠缠探针，如GHZ、贝尔和NOON态。实际量子态层析成像（QST）会产生含许多小有限测量和噪声诱导本征模的密度矩阵估计，导致本征值污染。我们引入用于量子态层析成像的谱子空间纯化（SSP-QST），它是最小二乘量子态层析成像（LS-QST）的秩自适应后处理层。通过对最小二乘估计进行特征分解等操作，无需秩先验等。在Qiskit Aer模拟中，SSP-QST在测试的非迭代基线中实现最高保真度，最大保真度增益为 +0.584，还提高了测量效率。结果表明SSP-QST可使光子QST在有限测量噪声下更可靠，为量子传感管道提供轻量级重建原语。
英文摘要
Photonic quantum sensing often uses low-rank entangled probes such as Greenberger-Horne-Zeilinger (GHZ), Bell, and NOON states. Although these probes are ideally rank-1, practical quantum state tomography (QST) can produce density-matrix estimates with many small finite-shot and noise-induced eigenmodes. This eigenvalue contamination can increase the estimated entropy of the reconstruction and reduce the quantum Fisher information (QFI) available for downstream sensing, while fixed rank-1 purification can discard valid signal modes when real probes acquire additional signal modes. We introduce Spectral Subspace Purification for Quantum State Tomography (SSP-QST), a rank-adaptive post-processing layer for least-squares quantum state tomography (LS-QST). SSP-QST eigendecomposes the least-squares estimate, computes a Weyl-motivated noise floor from the measured spectrum and shot count, removes eigenmodes below this floor, and renormalises the retained subspace. It requires no rank prior, no iterative optimisation, and only one eigendecomposition. In Qiskit Aer simulations, SSP-QST achieves the highest fidelity among the tested non-iterative baselines across the evaluated probe ranks, with a maximum fidelity gain of $+0.584$. It also improves shot efficiency by at least $8\times$ within the tested range. These results show that SSP-QST can make photonic QST more reliable under finite-shot noise while providing a lightweight reconstruction primitive for feedback-oriented quantum sensing pipelines.
