arXiv subjects

José Iovino

Publications and source records attributed to José Iovino.

8 recordsLinked to original sources

arXiv2026

Classification of bipartite observables I: stable and uniformly stable observables

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.

math.FA↗

arXiv2026

Classification of bipartite observables II: NIP observables and the Todorcevic trichotomy

This is the second 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 Shelah's independence property. An observable without it has idealized responses of the first Baire class, and Todorčević's trichotomy for Rosenthal compacta divides such observables into three classes, each containing a physical order. In the transverse-field Ising model, the spontaneous magnetization decides whether the family of magnetizations is stable or lies in the second class.

quant-ph↗

arXiv2026

Classification of bipartite observables III: simplicity, mixtures and quantum error correction

This is the third 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 simple unstable theories. The Pauli group of quantum error correction, with anticommutation as its relation, has a simple unstable theory, like the random graph. Forking and the Kim--Pillay independence theorem acquire a meaning in stabilizer codes: forking recognizes logical errors, and the independence theorem glues syndromes.

math.LO↗

arXiv2026

Complexity of deep computations via topology of function spaces

We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification of Rosenthal compacta, to identify new complexity classes. We use the language of model theory, specifically, the concept of \emph{independence} from Shelah's classification theory, to translate between topology and computation. We use the theory of Rosenthal compacta to characterize approximablility of deep computations, both deterministically and probabilistically.

math.LO↗

arXiv2014

Model Theory and the mean ergodic theorem for abelian unitary actions

We explore connections between von Neumann's mean ergodic theorem and concepts of model theory. As an application we present a proof Wiener's generalization of von Neumann's result in which the group acting on the Hilbert space $\mathcal{H}$ is any abelian group of unitary transformations of $\mathcal{H}$.

math.LO↗

arXiv2013

Ultraproducts and metastability

Given a convergence theorem in analysis, under very general conditions a model-theoretic compactness argument implies that there is a uniform bound on the rate of metastability. We illustrate with three examples from ergodic theory.

math.FA↗

arXiv2012

Omitting uncountable types, and the strength of $[0,1]$-valued logics

We study $[0,1]$-valued logics that are closed under the Łukasiewicz-Pavelka connectives; our primary examples are the the continuous logic framework of Ben Yaacov and Usvyatsov \cite{Ben-Yaacov-Usvyatsov:2010} and the Łukasziewicz-Pavelka logic itself. The main result of the paper is a characterization of these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

math.LO↗

arXiv2008

Model theoretic forcing in analysis

We present a framework for model theoretic forcing in a non-first-order context, and present some applications of this framework to Banach space theory.

math.LO↗