Quantum nonseparability is central to most philosophical puzzles related to quantum mechanics. Yet, it is not an exclusive property of quantum mechanics, as it is also found in theoretical generalizations thereof. Investigating the implications of quantum nonseparability in a broader context could shed a new light on the conceptual problems in quantum physics. This work focuses on an operational theory called the process matrix formalism that generalizes quantum mechanics by relaxing the assumption of a well-defined causal structure. That broader theoretical context allows for the existence of quantum processes that are causally nonseparable, i.e. for which there is no definite global causal order among its interacting elements. Therefore, this notion of causal nonseparability somehow extends the notion of entanglement to the geometry of spacetime.
This thesis is an examination of the measurement problem from within the Copenhagen interpretation of quantum mechanics where I take issue with von Neumann’s theory of measurement which argues for the subjective collapse of the wave function by a conscious observer. I argue that von Neumann’s postulate of collapse has led to several intractable philosophical and conceptual problems in its account of quantum measurement. I argue that these problems arise from von Neumann’s misreading of Bohr’s complementarity regarding the relationship between subject and object as distinct metaphysical entities. Instead, I offer a new way of defining the subject-object relation based on Don Howard’s reading of Bohr’s complementarity as subject-object nonseparability (SON). I argue that the SON principle has the potential of placing Copenhagen on more solid philosophical footing by viewing the subject-object relationship not as a causal relation, but as a relation of ontological dependence to avoid the idea of collapse altogether.
We investigate
k-nonseparability of
n-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some
k-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of
k-nonseparability through several examples.