Geometric Classification of Biased Quantum Capacity via Harmonic Translation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908907283152896 |
|---|---|
| author | Rosales, Eliseo Sarmiento Maximenko, Egor Molina, Dionisio Manuel Tun Cervantes, Juan Carlos Jimenez Vega, Jose Alberto Guzman Morales, Rodrigo Leon |
| author_facet | Rosales, Eliseo Sarmiento Maximenko, Egor Molina, Dionisio Manuel Tun Cervantes, Juan Carlos Jimenez Vega, Jose Alberto Guzman Morales, Rodrigo Leon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22336 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Classification of Biased Quantum Capacity via Harmonic Translation Rosales, Eliseo Sarmiento Maximenko, Egor Molina, Dionisio Manuel Tun Cervantes, Juan Carlos Jimenez Vega, Jose Alberto Guzman Morales, Rodrigo Leon Quantum Physics Information Theory 94B60, 81P70, 43A25 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. |
| title | Geometric Classification of Biased Quantum Capacity via Harmonic Translation |
| topic | Quantum Physics Information Theory 94B60, 81P70, 43A25 |
| url | https://arxiv.org/abs/2603.22336 |