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The Signal Horizon: Local Blindness and the Contraction of Pauli-Weight Spectra in Noisy Quantum Encodings

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.

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