H2020Индивидуална стипендия2021–2023

NONLOCQUANT · Nonlocality in quantum groups

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2021-06-01 → 2023-05-31
Финансиране от ЕС: 207 312 €
Участници: 1
Схема: MSCA-IF

Линиите свързват координатора с партньорите.

Накратко на български

Квантовите симетрии на графите изследват дали две мрежи от точки могат да изглеждат еднакви чрез квантови стратегии, дори да не са идентични. Това помага за по-доброто разбиране на връзките между квантовата информация и математическата теория на групите.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Nonlocality in quantum groups

Quantum symmetries of finite spaces were first characterized by Wang in 1997 using compact quantum groups. This led to the definition of the quantum symmetric group. Motivated by this, Banica and Bichon introduced quantum automorphism groups of finite graphs, capturing their quantum symmetries. Recently, connections to the isomorphism game, a nonlocal game constructed by Atserias et al., were drawn. The project „Nonlocality in quantum groups“ was to further investigate those connections. The first objective was to study quantum symmetries and nonlocal symmetries of graphs. Nonlocal symmetries are quantum symmetries that can be observed by players of the associated isomorphism game. The goals include finding new quantum isomorphic, non-isomorphic graphs and a graph with quantum symmetry and trivial automorphism group. The second objective focused on self-testing. In nonlocal games, self-testing results guarantee that optimal quantum strategies of a nonlocal game are unique, in some sense. In a third objective, we wanted to use quantum information theoretic tools for quantum groups, to further foster exchange between the areas.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

This project focuses on quantum automorphism groups of graphs and their connection to isomorphism games. We will investigate physically observable quantum behaviours, prove self-testing theorems and foster a two-way exchange between quantum groups and quantum information. The latter connection relies on quantum isomorphisms of graphs, which are defined as perfect quantum strategies of isomorphism games. Quantum isomorphisms from a graph to itself have been shown to be equivalent to quantum automorphisms, in the setting of quantum automorphism groups. One of the main questions that the project aims to understand are nonlocal symmetries of graphs. Those are quantum symmetries of graphs coming from non-classical quantum strategies of the corresponding isomorphism game. Interestingly, there are graphs that have quantum symmetry, but all quantum strategies are equivalent to classical ones. Thus, there is a difference between the considered model of reality and our observations of reality. Understanding this phenomenon will enable us to provide new examples of pairs of quantum isomorphic, non-isomorphic graphs. Another objective is to obtain self-testing theorems for isomorphism games. In the language of nonlocal games, self-testing means that any near perfect strategy is close to some fixed reference strategy. Self-testing theorems of linear binary constraint systems will be studied to transfer them to the isomorphism game setting. The project aims also to use recent results in quantum information theory for addressing open questions in quantum groups. On the one hand, giving examples of quantum automorphism groups of graphs that are not residually finite dimensional. On the other hand, figuring out the complexity of computing quantum symmetry and nonlocal symmetry.

Оригинален текст от CORDIS (на английски).

Участници

KOBENHAVNS UNIVERSITET · KOBENHAVNКоординаторДания