Parts and Wholes: An Inquiry into Quantum and Classical Correlations

Abstract

The primary topic of this dissertation is, firstly, the study of the correlations between outcomes of measurements on the subsystems of a composed system as predicted by a particular physical theory; secondly, the study of what this physical theory predicts for the relationships these subsystems can have to the composed system they are a part of; and thirdly, the comparison of different physical theories with respect to these two aspects. The physical theories investigated and compared are generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. The motivation for these enquiries is that a comparison of the relationships between parts and whole as described by each theory, and of the correlations predicted by each theory between separated subsystems yields a fruitful method to investigate what these physical theories say about the world. One then finds, independent of any physical model, relationships and constraints that capture the essential physical assumptions and structural aspects of the theory in question. As such one gains a larger and deeper understanding of the different physical theories under investigation and of what they say about the world. A large part of this dissertation is devoted to understanding different aspects of different kinds of correlations that can exist between the outcomes of measurement on subsystems of a larger system. Four different kinds of correlation have been investigated: local, partially-local, no-signaling and quantum mechanical. Novel characteristics of these correlations have been used to study how they are related and how they can be discerned. The main tool of this investigation has been the usage of Bell-type inequalities that give non-trivial bounds on the strength of the correlations. The study of quantum correlations has also prompted us to study the multi-partite qubit state space with respect to its entanglement and separability characteristics, and the differing strength of the correlations in separable and entangled qubit states. Comparing the different types of correlations has provided us with many new results on the various strengths of the different types of correlation. Because of the generality of the investigation -- we have considered abstract general models, not some specific and particular ones -- these results have strong repercussions for different sorts of physical theories. These repercussions have foundational as well as philosophical impact, notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy.