Abstract
Here, we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) that never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated with the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude, whose structure in terms of single-particle amplitudes we derive here by first principles. To characterize entanglement among the identical particles, this new method uses the same notions, such as partial trace, adopted for non-identical ones. We highlight the connection between our approach and second quantization. We also define spin-exchanged multipartite states which contain a generalization of W states to identical particles. We prove that particle spatial overlap plays a role in the distributed entanglement within multipartite systems and is responsible for the appearance of non-local quantum correlations.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
Highlights
We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated with the standard quantum mechanical treatment of identical particles
We have presented an alternative way to deal with sets of identical quantum objects
These objects, which can constitute building blocks of a complex system, can be considered as ‘particles’ in general, not coinciding with elementary excitations of quantum fields. This non-standard approach (NSA) to identical particles differs from the standard quantum mechanical approach (SA) one in that it never makes use of labels to mark particles
Summary
Identical quantum objects (e.g. qubits, atoms, quantum dots, photons, electrons and quasi-particles) typically. The global state of the two identical particles |Ψ0+ , when expressed in terms of labelled particles, has the form of an entangled state even if they are independently prepared far away from each other and never interact In other words, it seems that in the standard operational framework based on local operations and classical communication (LOCC), these two particles become entangled even if they are in a separable state at the beginning. The viewpoint of the SA makes a straightforward discussion of correlations (such as entanglement) in systems of identical particles problematic, because of the difficulty in formally separating the real part of correlations from the unphysical one arising from labels Such a description hinders the use of a partial trace and the von Neumann entropy, as normally done for non-identical particles [16]. This issue has originated different treatments for a faithful quantification of identical particle entanglement [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]
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