Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, the concomitant quantum statistics and their entanglement. Here, we (...) analyse the role of indistinguishability and non-individuality in other areas of quantum theory. We start by analysing how a very peculiar use of indistinguishability underlies Feynman’s rules for summing amplitudes in interference phenomena. Next, we study how quantum indistinguishability is underestimated in several topics of debate in the quantum physics literature, such as the Einstein–Podolsky–Rosen argument, Bell’s inequalities and the Bell–Kochen–Specker theorem. Finally, we argue that an ontology of truly indistinguishable entities can serve as a basis for a quantum ontology that can give interesting answers to the interpretational problems of quantum mechanics. We claim that, in addition to superposition, contextuality and entanglement, indistinguishability (understood in a robust ontological sense) is one of the central features of quantum physics. -/- . (shrink)

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology (...) in order to study the properties of quantum systems. (shrink)