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arXiv:1802.05826 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Dealing with indistinguishable particles and their entanglement

G. Compagno, Alessia Castellini, Rosario Lo Franco

Published May 28, 2018• 44 citations
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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'.

DOI
10.1098/rsta.2017.0317

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arXiv:1901.04938•Italian Quantum Information Science Conference (IQIS)•Jul 22, 2019•1 citation
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'.
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 study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.
There is a debate ongoing about the quantification of entanglement of indistinguishable particles, and recently a new method due to Lo Franco and Compagno (LFC) [Sci. Rep. 6, 20603 (2016)] has appeared with the aim of settling the controversies of this debate. In this work we show that the LFC approach can be recovered using the second quantization formalism and a local single-particle basis to perform the trace over a one-particle state. The use of the second quantization formalism has the advantage of being well known in many-body physics. We also compare the LFC and second quantization approaches or, equivalently, the effect of the partial trace over one particle depending on the local and nonlocal character of the single-particle basis. Additionally, we study the role played by the exchange correlations in the quantification of entanglement of indistinguishable particles.
The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics.Because of their exchange symmetry, identical particles can appear to be entangled-another uniquely quantum phenomenon with far-reaching practical implications.However, a long-standing debate has questioned whether identical particle entanglement is physical or merely a mathematical artifact.In this work, we provide such particle entanglement with a consistent theoretical description as a quantum resource in processes frequently encountered in optical and cold atomic systems.This leads to a plethora of applications of immediate practical impact.On the one hand, we show that the metrological advantage for estimating phase shifts in systems of identical bosons amounts to a measure of their particle entanglement, with a clear-cut operational meaning.On the other hand, we demonstrate in general terms that particle entanglement is the property resulting in directly usable mode entanglement when distributed to separated parties, with particle conservation laws in play.Application of our tools to an experimental implementation with Bose-Einstein condensates leads to the first quantitative estimation of identical particle entanglement.Further connections are revealed between particle entanglement and other resources such as optical nonclassicality and quantum coherence.Overall, this work marks a resolutive step in the ongoing debate by delivering a unifying conceptual and practical understanding of entanglement between identical particles.
Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles’ indistinguishability has been shown to be at the heart of various fundamental physical results. When concerned with the spatial degree of freedom, identical constituents can be made indistinguishable by overlapping their spatial wave functions via appropriately defined spatial deformations . By the laws of quantum mechanics, any measurement designed to resolve a quantity which depends on the spatial degree of freedom only and performed on the regions of overlap is not able to assign the measured outcome to one specific particle within the system. The result is an entangled state where the measured property is shared between the identical constituents. In this work, we present a coherent formalization of the concept of deformation in a general N -particle scenario, together with a suitable measure of the degree of indistinguishability. We highlight the basic differences with non-identical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the spatially localized operations and classical communication operational framework. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.
Quantum correlations of identical particles are important for quantum-enhanced technologies. The recently introduced non-standard approach to treat identical particles is here exploited to show the effect of particle indistinguishability on the characterization of entanglement of three identical qubits. We show that, by spatially localized measurements in separated regions, three independently-prepared separated qubits in a pure elementary state behave as distinguishable ones, as expected. On the other hand, delocalized measurements make it emerge a measurement-induced entanglement. We then find that three independently-prepared boson qubits under complete spatial overlap exhibit genuine three-partite entanglement. These results evidence the effect of spatial overlap on identical particle entanglement and show that the latter depends on both the quantum state and the type of measurement.