Bell nonlocality

Bell's theorem answers quantitatively, and in the negative, the question posed by Einstein, Podolsky, and Rosen, of whether there could be a deterministic description of nature with degrees of freedom, local in space, whose values are generally hidden from view. This review gives a comprehensive survey of contemporary formulations of the Bell inequalities, and various characterizations of the degree of nonlocality that are present in quantum theory, or that could be present in any conceivable postquantum theory. Implications for experiments, and for the science of cryptography, are also reviewed. 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. 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 subfield of quantum information science are reviewed.