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arXiv:2602.14735

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

Ait Haddou Marwan

quant-phcs.LGSubmitted Feb 16, 2026• Announced Feb 17, 2026• 0 citations• Revised Aug 4, 2026 (v2)
v1 · Feb 16, 2026v2 · Aug 4, 2026
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Abstract

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.

Comments
The manuscript is withdrawn because subsequent work showed that its central theoretical interpretation is incomplete. The relationship between local Pauli-weight contraction, measurement accessibility, and learnability requires a different theoretical framework. A substantially revised treatment is under preparation, and the current version should not be cited for these claims

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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 kkk subsystems. For nnn-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 kkk-local Pauli-accessible amplitude Ak(p)A_{k}(p)Ak​(p), which lower bounds the optimal kkk-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 kkk-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.
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Quantum classification faces two key challenges. First, the difficulty of distinguishing between different classes varies: some class pairs are easy to separate, while others are more challenging. Second, practical execution is affected by noise, finite sampling, and measurement overhead. To address these issues, we propose the Pauli-Space Discriminative-Representation based Quantum Classifier (PdrQC), a framework for task-adaptive multiclass quantum classification. The method evaluates candidate upload circuits using low-weight Pauli features and formulates upload design as a structured model selection problem based on discriminative representations. By progressively selecting upload structures and compact Pauli readout features for the target multiclass task, the framework achieves a better balance between classification accuracy and resource efficiency. Numerical simulations were conducted on the MNIST and Fashion-MNIST datasets with K∈{2,3,5,7,10}K\in\{2,3,5,7,10\}K∈{2,3,5,7,10}. The results demonstrate that PdrQC, through its task-adaptive Pauli representation, achieves an effective balance among multiclass classification accuracy, quantum-circuit complexity, and measurement overhead, making it suitable for multiclass quantum classification under limited hardware resources.
With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.
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