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Piccolini M, Nosrati F, Adesso G, Morandotti R, Lo Franco R. Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220104. [PMID: 37517442 DOI: 10.1098/rsta.2022.0104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 08/05/2022] [Indexed: 08/01/2023]
Abstract
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 [Formula: see text]-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'.
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Affiliation(s)
- Matteo Piccolini
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec, Canada J3X 1S2
| | - Farzam Nosrati
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec, Canada J3X 1S2
| | - Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, UK
| | - Roberto Morandotti
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec, Canada J3X 1S2
| | - Rosario Lo Franco
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy
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Catren G. Identity, individuality and indistinguishability in physics and mathematics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220109. [PMID: 37517434 PMCID: PMC10387373 DOI: 10.1098/rsta.2022.0109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 07/05/2023] [Indexed: 08/01/2023]
Abstract
In this brief survey, we discuss some of the scientific and philosophical problems and debates that underlie the notions of identity, individuality and indistinguishability in physics and mathematics. We critically analyse the different positions for or against the existence of indistinguishable objects in different scientific theories, notably quantum mechanics and gauge theories in physics and homotopy type theory in mathematics. We argue that the different forms of indistinguishability that occur in many areas of physics and mathematics-far from being a problem to be eradicated-exhibit a rich formal structure that plays a key role in the corresponding theories that needs to be properly understood. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.
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Affiliation(s)
- Gabriel Catren
- Laboratoire SPHERE (UMR 7219), Université Paris Cité - CNRS, 8 Rue Albert Einstein, Bâtiment Olympe de Gouge, 75013 Paris, France
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Majtey AP, Valdés-Hernández A, Cuestas E. Indistinguishable entangled fermions: basics and future challenges. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220108. [PMID: 37517438 DOI: 10.1098/rsta.2022.0108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2022] [Accepted: 03/26/2023] [Indexed: 08/01/2023]
Abstract
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of exploiting quantum indistinguishability as a resource in quantum information theory. Impressive theoretical and experimental advances have been made in the last decades that bring us closer to a deeper comprehension and to a better control of entanglement. Yet, when it involves composites of indistinguishable quantum systems, the very meaning of entanglement, and hence its characterization, still finds controversy and lacks a widely accepted definition. The aim of the present paper is to introduce, within an accessible and self-contained exposition, the basic ideas behind one of the approaches advanced towards the construction of a coherent definition of entanglement in systems of indistinguishable particles, with focus on fermionic systems. We also inquire whether the corresponding tools developed for studying entanglement in identical-fermion systems can be exploited when analysing correlations in distinguishable-party systems, in which the complete information of the individual parts is not available. Further, we open the discussion on the broader problem of constructing a suitable framework that accommodates entanglement in the presence of generalized statistics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.
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Affiliation(s)
- Ana P Majtey
- Instituto de Física Enrique Gaviola, CONICET and Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba X5016LAE, Argentina
| | - Andrea Valdés-Hernández
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México, Mexico
| | - Eloisa Cuestas
- Instituto de Física Enrique Gaviola, CONICET and Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba X5016LAE, Argentina
- Quantum Systems Unit, OIST Graduate University, Onna,Okinawa 904-0495, Japan
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Activation of indistinguishability-based quantum coherence for enhanced metrological applications with particle statistics imprint. Proc Natl Acad Sci U S A 2022; 119:e2119765119. [PMID: 35594392 PMCID: PMC9173775 DOI: 10.1073/pnas.2119765119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022] Open
Abstract
Quantum coherence has a fundamentally different origin for nonidentical and identical particles since for the latter a unique contribution exists due to indistinguishability. Here we experimentally show how to exploit, in a controllable fashion, the contribution to quantum coherence stemming from spatial indistinguishability. Our experiment also directly proves, on the same footing, the different role of particle statistics (bosons or fermions) in supplying coherence-enabled advantage for quantum metrology. Ultimately, our results provide insights toward viable quantum-enhanced technologies based on tunable indistinguishability of identical building blocks. Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.
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Piccolini M, Nosrati F, Compagno G, Livreri P, Morandotti R, Lo Franco R. Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions. ENTROPY (BASEL, SWITZERLAND) 2021; 23:708. [PMID: 34204915 PMCID: PMC8227133 DOI: 10.3390/e23060708] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Revised: 05/26/2021] [Accepted: 06/01/2021] [Indexed: 11/30/2022]
Abstract
We address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show that spatial indistinguishability of identical qubits can be utilized within the sLOCC operational framework to partially recover the quantum correlations spoiled by the environment. A general behavior emerges: the higher the spatial indistinguishability achieved via deformation, the larger the amount of recovered entanglement.
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Affiliation(s)
- Matteo Piccolini
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy; (M.P.); (F.N.); (P.L.)
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada;
| | - Farzam Nosrati
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy; (M.P.); (F.N.); (P.L.)
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada;
| | - Giuseppe Compagno
- Dipartimento di Fisica e Chimica—Emilio Segrè, Università di Palermo, via Archirafi 36, 90123 Palermo, Italy;
| | - Patrizia Livreri
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy; (M.P.); (F.N.); (P.L.)
| | | | - Rosario Lo Franco
- Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy; (M.P.); (F.N.); (P.L.)
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Benatti F, Floreanini R, Marzolino U. Entanglement and Non-Locality in Quantum Protocols with Identical Particles. ENTROPY (BASEL, SWITZERLAND) 2021; 23:479. [PMID: 33919487 PMCID: PMC8074231 DOI: 10.3390/e23040479] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/09/2021] [Accepted: 04/13/2021] [Indexed: 11/16/2022]
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.
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Affiliation(s)
- Fabio Benatti
- Department of Physics, University of Trieste, 34151 Trieste, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
| | - Roberto Floreanini
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
| | - Ugo Marzolino
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
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Barros MR, Chin S, Pramanik T, Lim HT, Cho YW, Huh J, Kim YS. Entangling bosons through particle indistinguishability and spatial overlap. OPTICS EXPRESS 2020; 28:38083-38092. [PMID: 33379628 DOI: 10.1364/oe.410361] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 11/05/2020] [Indexed: 06/12/2023]
Abstract
Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in the same system. While recent theoretical studies have shown that the spatial overlap between identical particles is necessary for nontrivial entanglement, the exact role of particle indistinguishability in the entanglement of identical particles has never been analyzed quantitatively before. Here, we theoretically and experimentally investigate the behavior of entanglement between two bosons as spatial overlap and indistinguishability simultaneously vary. The theoretical computation of entanglement for generic two bosons with pseudospins is verified experimentally in a photonic system. Our results show that the amount of entanglement is a monotonically increasing function of both quantities. We expect that our work provides an insight into deciphering the role of the entanglement in quantum networks that consist of identical particles.
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Sun K, Wang Y, Liu ZH, Xu XY, Xu JS, Li CF, Guo GC, Castellini A, Nosrati F, Compagno G, Lo Franco R. Experimental quantum entanglement and teleportation by tuning remote spatial indistinguishability of independent photons. OPTICS LETTERS 2020; 45:6410-6413. [PMID: 33258824 DOI: 10.1364/ol.401735] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 10/13/2020] [Indexed: 06/12/2023]
Abstract
Quantitative control of spatial indistinguishability of identical subsystems as a direct quantum resource at distant sites has not yet been experimentally proven. We design a setup capable of tuning remote spatial indistinguishability of two independent photons by individually adjusting their spatial distribution in two distant regions, leading to polarization entanglement from uncorrelated photons. This is achieved by spatially localized operations and classical communication on photons that meet only at the detectors. The amount of entanglement depends uniquely on the degree of spatial indistinguishability, quantified by an entropic measure I, which enables teleportation with fidelities above the classical threshold. The results open the way to viable indistinguishability-enhanced quantum information processing.
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Indistinguishability and Negative Probabilities. ENTROPY 2020; 22:e22080829. [PMID: 33286600 PMCID: PMC7517418 DOI: 10.3390/e22080829] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 07/27/2020] [Accepted: 07/28/2020] [Indexed: 11/17/2022]
Abstract
In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.
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Identical Quantum Particles, Entanglement, and Individuality. ENTROPY 2020; 22:e22020134. [PMID: 33285909 PMCID: PMC7516542 DOI: 10.3390/e22020134] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Revised: 01/06/2020] [Accepted: 01/12/2020] [Indexed: 11/17/2022]
Abstract
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind (“identical particles”) are completely indistinguishable from each other and lack identity. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of “particle” in ordinary language and in classical physical theory, but also with how this term is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by “particles” in the classical limit of quantum mechanics. Elaborating on earlier work, we here analyze the premises of the standard view and discuss an alternative that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory.
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Blasiak P, Markiewicz M. Entangling three qubits without ever touching. Sci Rep 2019; 9:20131. [PMID: 31882584 PMCID: PMC6934615 DOI: 10.1038/s41598-019-55137-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 10/30/2019] [Indexed: 11/09/2022] Open
Abstract
All identical particles are inherently correlated from the outset, regardless of how far apart their creation took place. In this paper, this fact is used for extraction of entanglement from independent particles unaffected by any interactions. Specifically, we are concerned with operational schemes for generation of all tripartite entangled states, essentially the GHZ state and the W state, which prevent the particles from touching one another over the entire evolution. The protocols discussed in the paper require only three particles in linear optical setups with equal efficiency for boson, fermion or anyon statistics. Within this framework indistinguishability of particles presents itself as a useful resource of entanglement accessible for practical applications.
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Affiliation(s)
- Pawel Blasiak
- Institute of Nuclear Physics Polish Academy of Sciences, PL-31342, Kraków, Poland.
- City, University of London, London, EC1V OHB, UK.
| | - Marcin Markiewicz
- Institute of Physics, Jagiellonian University, PL-30348, Kraków, Poland
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Adesso G, Franco RL, Parigi V. Foundations of quantum mechanics and their impact on contemporary society. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:20180112. [PMID: 29807907 PMCID: PMC5990657 DOI: 10.1098/rsta.2018.0112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/24/2018] [Indexed: 05/23/2023]
Affiliation(s)
- Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, UK
| | - Rosario Lo Franco
- Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Università di Palermo, Viale delle Scienze, Edificio 9, 90128 Palermo, Italy
- Dipartimento di Fisica e Chimica, Università di Palermo, via Archirafi 36, 90123 Palermo, Italy
| | - Valentina Parigi
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75252 Paris, France
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