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Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Correctionsquantum-computing

Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections

--> Quantum Physics arXiv:2608.18420 (quant-ph) [Submitted on 19 Aug 2026] Title:Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections Authors:Yixin Zhao, Fei Yan View a PDF of the paper titled Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections, by Yixin Zhao and 1 other authors View PDF HTML (experimental) Abstract:Maximum-probability (MP) decoding selects the most probable microscopic error, whereas degenerate maximum-likelihood (MLD) decoding includes the configurational entropy of an entire logical sector. Using code-capacity Pauli noise to isolate rigidity intrinsic to the code, we determine the first physical error weight $m$ at which their logical winner sets become disjoint, even under optimal MP tie resolution. Code distance imposes the universal bound $m\geq h=\lceil d/2\rceil$. We define the entropic rigidity depth $r$ through $m=h+r$ and certify a three-level hierarchy: $r=0$ for planar surface codes and two concatenated families, $r=1$ for odd-distance square toric codes and the Gross $[[144,12,12]]$ quantum low-density-parity-check code, and $r=2$ for a separable family with hypergraph product and bivariate bicycle descriptions. The onset fixes the leading operational failure gap, proportional to the $m$th power of the physical noise strength. Geometry and algebra therefore provide quantifiable controls of configurational entropy and an exact benchmark for low-noise decoder selection. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2608.18420 [quant-ph]   (or arXiv:2608.18420v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2608.18420 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yixin Zhao [view email] [v1] Wed, 19 Aug 2026 01:17:59 UTC (443 KB) Full-text links: Access Paper: View a PDF of the paper titled Ent

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Asymptotic Entanglement Hiding under Stabilizer Restrictionsquantum-computing

Asymptotic Entanglement Hiding under Stabilizer Restrictions

--> Quantum Physics arXiv:2608.18440 (quant-ph) [Submitted on 19 Aug 2026] Title:Asymptotic Entanglement Hiding under Stabilizer Restrictions Authors:Jicun Li, Wei Xie, Jun Wu, Honglin Chen, Xiang-Yang Li View a PDF of the paper titled Asymptotic Entanglement Hiding under Stabilizer Restrictions, by Jicun Li and 4 other authors View PDF HTML (experimental) Abstract:Entanglement is central to quantum information processing, while stabilizer operations underpin fault-tolerant quantum computation. We ask how much entanglement remains visible or distillable under stabilizer restrictions. We quantify stabilizer-visible entanglement by restricting the measured relative entropy of entanglement to stabilizer measurements, thereby obtaining converse bounds on entanglement distillation under stabilizer operations. We demonstrate magic-free asymptotic entanglement hiding: we construct explicit convex mixtures of pure stabilizer states on $N$ qutrits per party whose unrestricted visible entanglement and LOCC-distillable entanglement both grow as $\Omega(N/\log N)$, while their stabilizer-visible and stabilizer-distillable entanglement vanish as $N\to\infty$. Thus, an unbounded amount of LOCC-distillable entanglement carried by stabilizer states can become asymptotically invisible and undistillable under stabilizer restrictions. We further prove that stabilizer-visible entanglement is $O(1)$ with high probability for Haar-random pure states despite extensive unrestricted visibility, and vanishes uniformly over entangled Werner states as the local dimension grows through odd primes. These results reveal a fundamental separation between entanglement and magic as resources, exposing intrinsic limits on entanglement extraction using stabilizer operations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.18440 [quant-ph]   (or arXiv:2608.18440v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2608.18440 Focus to learn more arXiv-issued DOI vi

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