Geometric Classification of Biased Quantum Capacity via Harmonic Translation

Quantum Physics [Submitted on 21 Mar 2026] Geometric Classification of Biased Quantum Capacity via Harmonic Translation Eliseo Sarmiento Rosales, Egor Maximenko, Dionisio Manuel Tun Molina, Juan Carlos Jimenez Cervantes, Jose Alberto Guzman Vega, Rodrigo Leon Morales We establish an exact noise-model-derived characterization of quantum error correction under diagonal local phase noise. Under uniform locality, the maximal logical dimension under t-local phase errors equals Aq(n,2t+1), the classical q-ary packing function. Because no affine or stabilizer structure is imposed, nonlinear spectral supports achieve this bound and strictly exceed all affine constructions whenever Aq(n,2t+1)>Bq(n,2t+1). This follows from a harmonic translation principle: diagonal phase operators act as rigid translations in the Fourier domain, reducing the Knill-Laflamme conditions exactly to an additive non-collision constraint (S-S) cap Et={0}. For structured phase noise, exact correction is equivalent to independence in an additive Cayley graph, connecting biased quantum capacity to classical zero-error theory and the Lovasz theta function. Under mixed Pauli noise, simultaneous protection in conjugate domains incurs an intrinsic rate penalty R <= 1-(gamma_X+gamma_Z)/2, exposing a discrete harmonic uncertainty principle. In contrast with stabilizer- or graph-based frameworks, this classical correspondence is derived directly from the phase-noise model itself rather than from an auxiliary algebraic construction. Comments: 21 pages, 1 figure Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) MSC classes: 94B60, 81P70, 43A25 Cite as: arXiv:2603.22336 [quant-ph]   (or arXiv:2603.22336v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22336 Focus to learn more Submission history From: Eliseo Sarmiento [view email] [v1] Sat, 21 Mar 2026 04:17:42 UTC (44 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)