Algebraic geometry of quantum graphical models

• Tipo: Artigo em Revista Científica Internacional
• Data: 2025

Autores

Duarte, E (Autor) FCUP; Pavlov, D (Autor) Outra; Wiesmann, M (Autor) Outra

Revista

Título: Advances in Applied Mathematics

Vol. 170

ISSN: 0196-8858

Editora: Elsevier

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-019-HM6

DOI: 10.1016/j.aam.2025.102930

Abstract (EN): Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical models are families of quantum states satisfying certain locality or correlation conditions encoded by a graph. We lay out several ways to associate an algebraic variety to a quantum graphical model. The classical graphical models can be recovered from most of these varieties by restricting to quantum states represented by diagonal matrices. We study fundamental properties of these varieties and provide algorithms to compute their defining equations. Moreover, we study quantum information projections to quantum exponential families defined by graphs and prove a quantum analogue of Birch's Theorem. (c) 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 25