Classification of bipartite observables I: stable and uniformly stable observables
Abstract
This is the first of a series of three papers that bring model theory to quantum information. The dividing lines of Shelah's classification theory, which separate the tame first-order theories from the wild ones, become properties of bipartite observables: properties of the expectation values obtained when two independently prepared quantum systems are idealized one after the other. In this paper we focus on stability. An observable is stable when the order in which the two systems are idealized never changes its expectation value, and this is Shelah's stability. Its classical characterizations, in model theory and in analysis, acquire a physical meaning: idealized preparations are simulated by finite mixtures of actual ones, and adaptive probes can tell apart only polynomially many preparations.
Related
- Classification of bipartite observables II: NIP observables and the Todorcevic trichotomy
- Classification of bipartite observables III: simplicity, mixtures and quantum error correction
- Strictly stable solutions in uniformly convex planar domains may have nonconvex superlevel sets
- Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms
- P-stable degree sequence regions for bipartite and directed graphs
BibTeX
@misc{duenez2026classification,
title = {{Classification of bipartite observables I: stable and uniformly stable observables}},
author = {Eduardo Dueñez and José Iovino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11002},
eprint = {2610.11002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification of bipartite observables I: stable and uniformly stable observables
AU - Eduardo Dueñez
AU - José Iovino
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.11002
UR - https://arxiv.org/abs/2610.11002
AB - This is the first of a series of three papers that bring model theory to quantum information. The dividing lines of Shelah's classification theory, which separate the tame first-order theories from the wild ones, become properties of bipartite observables: properties of the expectation values obtained when two independently prepared quantum systems are idealized one after the other. In this paper we focus on stability. An observable is stable when the order in which the two systems are idealized never changes its expectation value, and this is Shelah's stability. Its classical characterizations, in model theory and in analysis, acquire a physical meaning: idealized preparations are simulated by finite mixtures of actual ones, and adaptive probes can tell apart only polynomially many preparations.
ER -