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arXiv:2104.06154 · Entropy

Entanglement and Non-Locality in Quantum Protocols with Identical Particles

Fabio Benatti, Roberto Floreanini B, Ugo Marzolino

Published Apr 18, 2021• 5 citations
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Abstract

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.

DOI
10.3390/e23040479

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We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.
Unlike for bipartite states consisting of distinguishable particles, in the case of identical parties the notion of entanglement is still under debate. In the following, we review two different approaches to the entanglement of systems consisting of two bosons or fermions; the first approach is based on the particle aspect typical of first quantization and identifies separable pure states as those that allow to assign two orthogonal single particle vector states to both parties. The second approach makes full use of the mode aspect of second quantization whereby separability can be formulated as absence of nonlocal correlation among two different sets of modes. While the first approach applies to pure states only, the second one is more general and characterizes generic entangled states. In the following, we shall show that the mode-based approach indeed contains the particle-based one.
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'.
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'.
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based methods have been developed that attempt to overcome the issue. Here we introduce a state-based method which, as second quantization, does not label identical particles and presents conceptual and technical advances compared to the previous ones. It establishes the quantitative role played by arbitrary wave function overlaps, local measurements and particle nature (bosons or fermions) in assessing entanglement by notions commonly used in quantum information theory for distinguishable particles, like partial trace. Our approach furthermore shows that bringing identical particles into the same spatial location functions as an entangling gate, providing fundamental theoretical support to recent experimental observations with ultracold atoms. These results pave the way to set and interpret experiments for utilizing quantum correlations in realistic scenarios where overlap of particles can count, as in Bose-Einstein condensates, quantum dots and biological molecular aggregates.
We argue that in the case of identical particles the most natural identification of separability, that is of absence of non-classical correlations, is via the factorization of mean values of commuting observables. It thus follows that separability and entanglement depend both on the state and on the choice of observables and are not absolute notions. We compare this point of view with a recent novel approach to the entanglement of identical particles, which allows for the definition of an entanglement entropy from a suitably defined reduced particle density matrix, without the need of labelling the system constituents. We contrast this figure of merit with the aforementioned lack of an absolute notion of entanglement by considering few paradigmatic examples.
Identical particles and entanglement are both fundamental components of quantum mechanics. However, when identical particles are condensed in a single spatial mode, the standard notions of entanglement, based on clearly identifiable subsystems, break down. This has led many to conclude that such systems have limited value for quantum information tasks, compared to distinguishable particle systems. To the contrary, we show that any entanglement formally appearing amongst the identical particles, including entanglement due purely to symmetrization, can be extracted into an entangled state of independent modes, which can then be applied to any task. In fact, the entanglement of the mode system is in one-to-one correspondence with the entanglement between the inaccessible identical particles. This settles the long-standing debate about the resource capabilities of such states, in particular spin-squeezed states of Bose-Einstein condensates, while also revealing a new perspective on how and when entanglement is generated in passive optical networks. Our results thus reveal new fundamental connections between entanglement, squeezing, and indistinguishability.