Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).

Principales puntos de convergencia entre las escuelas hegemónicas de teoría económica y sociológica desde la Ilustración escocesa hasta nuestros días

This research aims to show the main points of convergence between hegemonic schools of economic and sociological theory from the Scottish Enlightenment until today. To this end, on the one hand, we set three basic families of economic thought (the mainstream, the Austrian school and Marxism); and, on the other, we divide the history of sociology in five major generations (pioneers, founders, institutionalizers, compilers and constructivist). Subsequently, we set five historical periods as reference to our respective chapters and compare, within each of them, the theoretical contributions from these two areas. Thus, in the first chapter, called "the liberal parenthesis", we consider the relationship between the classical school of economics and the pioneers and founders of sociology. In the second, entitled "the social question" we analyze, on the one hand, the theoretical consistency of both the neoclassical school, as Austrian, with the principles defended by the institutionalizers of sociology; and, on the other, the influence of Karl Marx, as founder of sociology and classical economist, in the work of Soviet revolutionary theorists. In chapter three, called the "new industrial state", we demonstrate the theoretical proximity between both Keynesianism and the Austrian school of economics, with the doctrine defended by the generation of compilers in sociology. The fourth chapter, entitled "second industrial divide", refers to the similarities between the theoretical contributions of the monetarist Chicago school and the Austrian school with sociological constructivism. Finally, chapter five, the "global market", shows that the two hegemonic schools in economics, "integrated model", and sociology, "analytical sociology", are composed of the same three schools of thought: the rational choice, the neo-institutionalism and network approach. Thus, we can conclude that, if we look at their respective areas of influence, during this historical period occurs an manifest agreement between the theoretical contributions from the economic and sociological fields.