Quantum hedging in two-round prover-verifier interactions

We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either 'win' or 'lose'. Molina and Watrous (arXiv:1104.1140) studied such a game that exhibited a perfect form of hedging, where the risk of losing a first game can completely offset the corresponding risk for a second game. This is a non-classical quantum phenomenon, and establishes the impossibility of performing strong error-reduction for quantum interactive proof systems by parallel repetition, unlike for classical interactive proof systems. We take a step in this article towards a better understanding of the hedging phenomenon by giving a complete characterization of when perfect hedging is possible for a natural generalization of the game in arXiv:1104.1140. Exploring in a different direction the subject of quantum hedging, and motivated by implementation concerns regarding loss-tolerance, we also consider a variation of the protocol where the player who receives the question can choose to restart the game rather than return an answer. We show that in this setting there is no possible hedging for any game played with state spaces corresponding to finite-dimensional complex Euclidean spaces.Comment: 34 pages, 1 figure. Added work on connections with other result

Extended Nonlocal Games

The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly models a physical system. The simplest instance of a nonlocal game involves two players, Alice and Bob, who are not allowed to communicate with each other once the game has started and who play cooperatively against an adversary referred to as the referee. The focus of this thesis is a class of games called extended nonlocal games, of which nonlocal games are a subset. In an extended nonlocal game, the players initially share a tripartite state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to the questions sent by the referee. We build up the framework for extended nonlocal games and study their properties and how they relate to nonlocal games.Comment: PhD thesis, Univ Waterloo, 2017. 151 pages, 11 figure

Suivi de l’évolution thermique de la Méditerranée

Le but de ce travail de Bachelor est d’automatiser la récolte des données de relevé thermiques de la Méditerranée ainsi que leur stockage dans une base de données, et de fournir un moyen simple de visualisation de ces informations. ETAT DE L’ART Avant de débuter le développement du projet, il est nécessaire de rechercher, lister et comparer les différents outils déjà disponibles sur le marché. Chaque outil se différencie par sa palette de fonctionnalités, sa simplicité, son utilité, sa performance ou même son coût. Il est donc essentiel de passer par cette étape de recherche afin d’avoir une vue d’ensemble et de choisir les outils les mieux adaptés pour le projet. PROJET Le projet final est destiné à être installé au sein du CREALP, qui l’utilisera aux côtés de ses autres outils de surveillance. Les données seront : Téléchargées régulièrement Converties Insérées dans une base de données Affichées sur une page web interne La plupart des technologies utilisées dans ce projet sont imposées par le CREALP afin de correspondre au mieux à leur système et méthodes de travail. RAPPORT Le présent rapport détaille les recherches, les grandes étapes du projet ainsi que les fonctionnalités. Un CD-ROM est joint à ce rapport, contenant entre-autres, le code source ainsi que les outils utilisés

Is absolute separability determined by the partial transpose?

The absolute separability problem asks for a characterization of the quantum states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case that $\rho$ is absolutely separable if and only if $U\rho U^\dagger$ has positive partial transpose for all unitary matrices $U$. In particular, we develop an easy-to-use method for showing that an entanglement witness or positive map is unable to detect entanglement in any such state, and we apply our method to many well-known separability criteria, including the range criterion, the realignment criterion, the Choi map and its generalizations, and the Breuer-Hall map. We also show that these two properties coincide for the family of isotropic states, and several eigenvalue results for entanglement witnesses are proved along the way that are of independent interest.Comment: Two of our results were corrected since v2; the primary results of interest remain unchange