Bell nonlocality

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools which have been developed to describe and study the nonlocality of quantum theory, and which have raised this topic to the status of a full sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio

No-signalling attacks and implications for (quantum) nonlocality distillation

The phenomenon of nonlocality, which can arise when entangled quantum systems are suitably measured, is perhaps one of the most puzzling features of quantum theory to the philosophical mind. It implies that these measurement statistics cannot be explained by hidden variables, as requested by Einstein, and it thus suggests that our universe may not be, in principle, a well-determined entity where the uncertainty we perceive in physical observations stems only from our lack of knowledge of the whole. Besides its philosophical impact, nonlocality is also a resource for information- theoretic tasks since it implies secrecy: If nonlocality limits the predictive power that any hidden variable (in the universe) can have about some observations, then it limits in particular the predictive power of a hidden variable held by an adversary in a cryptographic scenario. We investigate whether nonlocality alone can empower two parties to perform unconditionally secure communication in a feasible manner when only a provably minimal set of assumptions are made for such a task to be possible — independently of the validity of any physical theory (such as quantum theory). Nonlocality has also been of interest in the study of foundations of quantum theory and the principles that stand beyond its mathematical formalism. In an attempt to single out quantum theory within a broader set of theories, the study of nonlocality may help to point out intuitive principles that distinguish it from the rest. In theories where the limits by which quantum theory constrains the strength of nonlocality are surpassed, many “principles” on which an information theorist would rely on are shattered — one example is the hierarchy of communication complexity as the latter becomes completely trivial once a certain degree of nonlocality is overstepped. In order to study the structure of such super-quantum theories — beyond their aforementioned secrecy aspects — we investigate the phenomenon of distillation of nonlocality, the ability to distill stronger forms of nonlocality from weaker ones. By exploiting the inherent connection between nonlocality and secrecy, we provide a novel way of deriving bounds on nonlocality-distillation protocols through an ad versarial view to the problem

Caracterización del entrelazamiento y no localidad cuánticos como recursos en sistemas multipartitos

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 14-07-2021Quantum technologies are enjoying an unprecedented popularity, and some applicationsare already in the market. This thesis studies two phenomena that are behind a lot ofquantum technologies: entanglement and nonlocality. We focus on multipartite systems,and ask what con gurations of those systems are more useful than others. `Usefulness'takes on dierent meanings depending on the context, but, roughly speaking, we aim formore entanglement or more nonlocality.Chapter 2 is motivated by an important issue with traditional resource theories ofmultipartite entanglement: they give rise to isolated states and inequivalent forms ofentanglement. We propose two new resource theories that do not give rise to theseproblems: the resource theory of non-full-separability under full separability-preservingoperations, and the resource theory of genuine multipartite entanglement (GME) underbiseparability-preserving operations. Further, the latter theory gives rise to a uniquemaximally GME state...Las tecnologías cuánticas gozan actualmente de una popularidad sin precedentes, y ya tienen aplicaciones en el mercado. Esta tesis estudia dos fenómenos que están detrás de muchas de estas tecnologías: el entrelazamiento y la no localidad. Nos centramos en sistemas multipartitos, y tratamos de averiguar qué configuraciones de estos sistemas son mas útiles. La noción de utilidad varía según el contexto pero, en términos generales, aspiramos a conseguir más entrelazamiento o más no localidad. El capítulo 2 viene motivado por un problema importante en las teorías de recursos de entrelazamiento multipartito tradicionales: dan lugar a estados aislados y a formas de entrelazamiento no equivalentes. En este capítulo proponemos dos nuevas teorías de recursos que no generan estos problemas: la teoría de recursos de no-separabilidad completa bajo operaciones que preservan separabilidad completa, y la teoría de recursos de entrelazamiento multipartito genuino (GME, por sus siglas en ingles) bajo operaciones que preservan biseparabilidad. Además, esta ultima teoría da lugar a un estado maximamente GME único...Fac. de Ciencias MatemáticasTRUEunpu

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys