This thesis explores various perspectives on quantum phenomena, and how our understanding of these phenomena is informed by the study of general probabilistic theories. Particular attention is given to quantum nonlocality, and its interaction with areas of physical and mathematical interest such as entropy, reversible dynamics, information-based games and the idea of negative probability. We begin with a review of non-signaling distributions and convex operational theories, including “black box” descriptions of experiments and the mathematics of convex vector spaces. In Chapter 3 we derive various classical and quantum-like quasiprobabilistic representations of arbitrary non-signaling distributions. Previously, results in which the density operator is allowed to become non-positive [1] have proved useful in derivations of quantum theory from physical requirements [2]; we derive a dual result in which the measurement operators instead are allowed to become non-positive, and show that the generation of any non-signaling distribution is possible using a fixed separable state with negligible correlation. We also derive two distinct “quasi-local” models of non-signaling correlations. Chapter 4 investigates non-local games, in particular the game known as Information Causality. By analysing the probability of success in this game, we prove the conjectured tightness of a bound given in [3] concerning how well entanglement allows us to perform the task of random access coding, and introduce a quadratic bias bound which seems to capture a great deal of information about the set of quantum-achievable correlations. By reformulating Information Causality in terms of entropies, we find that a sensible measure of entropy precludes many general probabilistic theories whose non-locality is stronger than that of quantum theory. Chapter 5 explores the role that reversible transitivity (the principle that any two pure states are joined by a reversible transformation) plays as a characteristic feature of quantum theory. It has previously been shown that in Boxworld, the theory allowing for the full set of non-signaling correlations, any reversible transformation on a restricted class of composite systems is merely a composition of relabellings of measurement choices and outcomes, and permutations of subsystems [4]. We develop a tabular description of Boxworld states and effects first introduced in [5], and use this to extend this reversibility result to any composite Boxworld system in which none of the subsystems are classical.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-06-29T11:57:33Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) template.pdf: 1023711 bytes, checksum: bb469b82eb53b63f6e13f942f61ae867 (MD5) / Made available in DSpace on 2016-06-29T11:57:33Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) template.pdf: 1023711 bytes, checksum: bb469b82eb53b63f6e13f942f61ae867 (MD5) Previous issue date: 2014-08-14 / CNPq / As fun c~oes de Bell s~ao conhecidas pelo papel central desempenhado na caracteriza c~ao da n~ao localidade da teoria qu^antica. Usualmente s~ao empregadas na quanti ca c~ao do grau de n~ao localidade de sistemas qu^anticos espec cos atrav es do calculo do seu valor m aximo entre todos os poss veis estados e con gura c~oes associadas aos detectores. No entanto, embora dois estados qu^anticos tenham diferentes \densidades de con gura c~ao n~ao local"( Estados com diferentes contribui c~oes de con gura c~oes associadas aos detectores que geram n~ao localidade), se eles possuem o mesmo valor do m aximo da fun c~ao de Bell, ent~ao s~ao considerados igualmente n~ao locais. Usando este crit erio, Ac n et al. (Phys. Rev. A 65, 052325, 2002) encontraram que para qunits (Estados de sistemas qu^anticos conjuntos d-dimensionais), o estado maximamente emaranhado n~ao corresponde ao estado maximamente n~ao local, fato que e considerado como uma anomalia da n~ao localidade da teoria qu^antica (M ethot & Scarani; Quant. Inf. Comput. 7, 157, 2008). A m de resolver o problema da anomalia, nesta disserta c~ao e proposta uma medida do grau de n~ao localidade, na qual s~ao tomadas em conta todas as contribui c~oes de con- gura c~oes dos detectores que geram n~ao localidade do estado. Tal medida e proporcional a integral da fun c~ao de Bell na regi~ao de viola c~ao, no espa co dos par^ametros que caracterizam as con gura c~oes (Em geral ^angulos relativos entre orienta c~oes dos detectores). Foi calculado o grau de n~ao localidade de v arios sistemas de dois e tr^es n veis, com e sem uma contribui c~ao de ru do qu^antico ao estado, usando tr^es tipos de desigualdades de Bell: A desigualdade na vers~ao original, a desigualdade CHSH e a desigualdade GCLMP (Ac n et al. 2002). Em todos os casos estudados foi observada concond^ancia entre o estado maximamente emaranhado e o estado maximamente n~ao local, resolvendo assim o problema da anomalia da n~ao localidade. / Bell functions are known by the central role played on the characterization of non-locality in quantum theory. They are often used in the quanti cation of the non-locality strength for speci c quantum systems by calculating their maximum among all possible states and detector's con gurations. However, even if two quantum states present di erent \nonlocal density con gurations"(States with di erent contributions of detector con gurations that generate non-locality), if these display the same value for the maximum of Bell function, then they are considered equally non-local. Making use of this criteria, Ac n et al. (Phys. Rev. A 65, 052325, 2002) found that for qunits (Joint states of d-dimensional quantum systems), the maximally entangled state does not match with the maximally non-local state, this is known as an anomaly of quantum non-locality (M ethot & Scarani; Quant. Inf. Comput. 7, 157, 2008). In order to solve the anomaly problem, in this dissertation it is proposed a nonlocality strength measure in which the whole contributions of detector's con gurations that give rise to non-locality are taken into account. Such a measure is proportional to the Bell function integration over the violation region on the space of the parameters that characterize the detector's con guration (Usually, relative angles between orientations of detectors). The non-locality strength was calculated for several two and three-level bipartite systems, with and without a contribution of white noise to the whole state of the system, by using three kinds of Bell inequalities: Bell inequality in its original version, CHSH inequality and GCLMP inequality (Ac n et al. 2002). In all the cases, it was observed agreement between maximally entangled states and maximally non-local ones, thus solving the problem of anomaly of non-locality.