信号视界：局部盲区与诺伊兹量子编码中泡利权重光谱的收缩
The Signal Horizon: Local Blindness and the Contraction of Pauli-Weight Spectra in Noisy Quantum Encodings
AI总结：
本研究探讨了噪声环境下局部测量对量子分类性能的影响，提出k局部泡利可及振幅作为预测分类优势的下界，并揭示了k局部分类器在特定噪声水平下的操作性崩溃阈值。
摘要：
量子分类器的性能通常通过全局态可区分性或变分模型的可训练性来分析。本研究探讨了在噪声存在下，局部受限测量条件下可保留多少类别信息。作者将二元量子分类视为受限量子态鉴别，并引入一个局部受限可区分性度量，量化了最多作用于k个子系统的可观测量所能达到的最大偏置。对于受独立去极化噪声影响的n量子比特系统，局部可访问的信号由泡利权重依赖的收缩机制所支配。这促使了可计算的预测器，即k局部泡利可及振幅A_k(p)，它下界了最优k局部分类优势。在四量子比特编码上的数值实验显示，在不同噪声水平下，实证准确率与预测之间存在定量一致。该研究识别了一个操作性崩溃阈值，在此阈值下，k局部分类器即使在全局可区分性持续存在的情况下，也变得与随机猜测无法区分。
英文摘要：
The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most $k$ subsystems. For $n$-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the $k$-local Pauli-accessible amplitude $A_{k}(p)$, which lower bounds the optimal $k$-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where $k$-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
