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Studies in History and Philosophy of Science Part A

Entanglement and indistinguishability in a quantum ontology of properties

Sebastián Fortín, Olímpia Lombardi

Published Dec 28, 2021• 34 citations
Publisher
DOI
10.1016/j.shpsa.2021.11.017

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While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguishability, even with respect to the definition of the concept of entanglement. Second, the fact that symmetrized and antisymmetrized states of indistinguishable particles are non-factorizable leads to certain perplexities about the very nature of entanglement. In the present work, both issues will be addressed from the perspective of an ontology of properties, which finds its natural expression in the algebraic formalism of quantum mechanics. The final goal will be to show that the proposed ontology allows a unified treatment of entanglement in the distinguishability and indistinguishability cases and offers a straightforward way out to perplexities. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

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Quantum ontology and intuitions

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While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguishability, even with respect to the definition of the concept of entanglement. Second, the fact that symmetrized and antisymmetrized states of indistinguishable particles are non-factorizable leads to certain perplexities about the very nature of entanglement. In the present work, both issues will be addressed from the perspective of an ontology of properties, which finds its natural expression in the algebraic formalism of quantum mechanics. The final goal will be to show that the proposed ontology allows a unified treatment of entanglement in the distinguishability and indistinguishability cases and offers a straightforward way out to perplexities. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.
In contrast to conventional, dynamical entanglement, in which particles with definite identity have uncertain properties, in so-called statistical entanglement, which arises between indistinguishable particles because of quantum symmetry rules, even particle identities are uncertain. The Bell and Kochen-Specker theorems imply that quantum properties either lack realism or possess it with a caveat of contextuality or nonlocality. In the matter of identity of multi-particle states of indistinguishable particles, these contrasting ontological attitudes are mirrored by the "bundle" vs. haecceity views. We offer some arguments aimed at importing the above theorems to the issue of identity in quantum theory, with the conclusion (under certain assumptions) that indistinguishable particles either lack individualism or possess a definite identity with a caveat of contextuality or nonlocality.
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. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.