Entanglement and Quantum Non-Locality

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The aim of this project is to gain a deeper understanding of two fundamental concepts of quantum physics: entanglement and non-locality. The evolution of both of these concepts during the last century is remarkable. While Einstein considered them as an evidence of the failure of quantum mechanics, they are now recognized as an amazingly powerful resource for processing information. They are at the core of Quantum Information Science, which has established itself as a new branch of modern physics. Entanglement is a quantum property that has no classical analog. Entangled states have the striking property that they can be used to establish non-local correlations. In other words, correlations that cannot be reproduced by any physical model that behaves locally, as shown by Bell in the 1960s. Today the situation is even more exciting, since it has been realized that non-locality and entanglement, for long considered as being different facets of the same phenomenon, are in fact very different concepts and resources. This new line of research is based on a pioneering work of Popescu and Rohrlich, who showed that there are nonsignaling correlations (correlations that do not permit to send information faster than light) that are more non-local than those of quantum physics. The project has three main objectives. First, it will focus on the relation between the concepts of entanglement and non-locality. Roughly speaking, entanglement is the resource for processing quantum information, while non-locality provides a good measure of its computational power. Indeed, it is crucial for Quantum Information Science to have a deep understanding between the resource and the power it offers. Here, the problem will be addressed using the idea of simulating entangled states. In other words, to construct an alternative model to quantum theory, that predicts the same result for any measurements performed on an entangled state. Then, the project will address the problem of testing the Hilbert space dimension. The Hilbert space is the abstract mathematical framework for describing quantum states. As intuition suggests, the dimension of this space is directly related to the complexity of the state, and also to its uselfulness for processing information. Here, the goal will be to find efficient techniques for testing the Hilbert space dimension of an unknown quantum system. Finally this research will explore the possibility to test entanglement in macroscopic physical systems, which is still a grand challenge. Indeed, while it may be acceptable that tiny particles have very counter-intuitive properties (such as entanglement), it becomes far more difficult to conceive for macroscopic objects. The goal of this research will be to find physical systems well-suited for an experimental demonstration of entanglement on the macroscopic level. This research will shine new light on the foundations of quantum physics, but will also to provide potentially useful application in Quantum Information Science.