Entanglement and indistinguishability in a quantum ontology of properties

OLIMPIA LOMBARDI; SEBASTIAN FORTIN

Buenos Aires

Simposio; X Conference on Quantum Foundations: Ten Irreversible Years of Quantum Foundations in Argentina; 2021

CONICET y CNRS

Entanglement in many-body systems of so-called "indistinguishableparticles" has received a great attention during the last decades due to itsapplications in quantum information andcondensed matter. These works have led to revise the veryconcept of entanglement in the case of indistinguishability, which posesa specific challenge: according to the traditional definition of entanglementin pure states as non-factorizability, symmetrized and anti-symmetrized statesshould be entangled (except in some cases involving bosons). But there are goodreasons to think that this is not the case: not always non-factorizable statesof composite bosonic or fermionic systems should be conceived as legitimatecases of entanglement.Thisproblem has been addressed from different perspectives, such as modifying thegeneral definition of entanglement, removing the "surplus structure" resultingfrom the need of symmetrize or anti-symmetrize states in the case ofindistinguishability, or rejecting the link between Hilbert space labels andquantum systems in the case of the components of a composite system.Nevertheless, the common feature of those proposals ‒as well as of thediscussions about the general problem of how to understandindistinguishability‒ is the way in which indistinguishability is conceived: "being indistinguishable from" refers to a relation between particles.The aim of the present talk is to address theproblem of entanglement in the case of indistinguishable particles from aperspective based on the algebraic formalism of quantum mechanics, which is thenatural formal counterpart of an ontology of properties, devoid of theontological category of individual. On the basis of this perspective, analgebraic definition of entanglement is adopted, which supplies a unifiedconception, valid for both the distinguishable and the indistinguishable cases.An additional advantage of this algebraic definition is that it does justice tothe relativity of entanglement, a feature that cannot be ignored.