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.

翻译：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进行分析。本研究探讨在噪声存在下，受限于局部测量的情况下，类别信息有多少仍然可访问。作者将二元量子分类表述为约束量子态区分问题，并引入一种局部受限的可区分性度量，该度量量化了最多作用于$k$个子系统的可观测量所能实现的最大偏差。对于受独立退极化噪声影响的$n$量子比特系统，局部可访问的信号由一种依赖于泡利权重的收缩机制所支配。这启发了一个可计算的预测器——$k$局部泡利可访问幅度$A_{k}(p)$，该预测器为最优$k$局部分类优势提供了下界。在四量子比特编码上的数值实验表明，在不同噪声水平下，经验准确率与该预测值之间存在定量一致性。该研究识别出一个操作崩溃阈值，在此阈值下，尽管全局可区分性仍然存在，$k$局部分类器变得与随机猜测无法区分。