Research Article · Preprint Mathematics
Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensions
- Primary subject
- Mathematics
- Subject subfields
- Quantum Information Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 3 · Permanent link
Overview
Abstract
We strengthen proper agnostic learning of stabilizer states for arbitrary mixed inputs in every odd-prime local dimension. Given an overlap promise F≥τ, the learner returns a pure stabilizer of overlap at least F-ε, with confidence 1-δ, using exp(O(log^2(2/τ))) poly(n,p,ε^(-1),log(2/δ)) resources with absolute exponent constants and fixed polynomial degree. The previous dimension-dependent exponent is removed by testing Weyl spectral concentration and selecting an observed eigenvalue. An even quotient-convolution argument also improves escape to (p-1)F^r/(4p), where r=6 for p≡3(mod 4) and r=4 for p≡1(mod 4), using the same known measurements. Explicit rational counters cover all rejection attempts and final validation. The model still uses exact Clifford operations and coherent eigenspace measurements. We attribute the measurement primitives, uncertainty ingredients and bootstrapping framework to prior work; the strengthening concerns their uniform quantitative combination.
Keywords stabilizer states · agnostic learning · quantum learning · mixed states · odd-prime dimensions
Scope of the work
Proper agnostic learning for arbitrary mixed inputs in every odd-prime local dimension with dimension-uniform exp(O(log²(2/τ))) resource exponents, and stronger quotient-convolution escape, in the stated exact Clifford/coherent-measurement model.
Reproduction notes
The paper has 10 pages. The editable-source archive contains 13 files. Compile manuscript/main.tex and read the complete supporting proof. Use Python with NumPy to run verification/verify_package.py, its --full diagnostic replay and robustness controls in fresh external directories.
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Author disclosures
Originality is qualified against the inspected literature; no worldwide priority, optimal-resource or practical-efficiency claim is made. Known weighted/skewed measurements, convolution tools and stabilizer bootstrapping are credited. Exact Clifford and coherent eigenspace operations are assumed; no noisy or compiled finite-gate theorem is proved. AI assistance was used in derivation, programming, literature discovery and proof checking. Internal reviews do not constitute external human refereeing or formal verification. Personal explanations and internal review records are excluded from the public package.
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Cite this edition
Scott Schubr. (2026). Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensions (Version 3). Luminary Research Archive. https://research.luminaryoddities.com/mixed-state-escape-bounds-proper-agnostic-learning-stabilizer-states-odd-prime-dimensions/v/3
BibTeX
@techreport{luminary_mixed_state_escape_bounds_proper_agnostic_learning_stabilizer_states_odd_prime_dimensions_v3,
title = {Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensions},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 3},
url = {https://research.luminaryoddities.com/mixed-state-escape-bounds-proper-agnostic-learning-stabilizer-states-odd-prime-dimensions/v/3}
}Loading discussion…