تقرير
Algebraic Geometry of Quantum Graphical Models
| العنوان: | Algebraic Geometry of Quantum Graphical Models |
|---|---|
| المؤلفون: | Duarte, Eliana, Pavlov, Dmitrii, Wiesmann, Maximilian |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Quantum Physics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Quantum Physics, 14Q99, 81P45, 62R01 |
| الوصف: | 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. Comment: 20 pages, comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.11538 |
| رقم الأكسشن: | edsarx.2308.11538 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |