1
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Bao Y, Block M, Altman E. Finite-Time Teleportation Phase Transition in Random Quantum Circuits. PHYSICAL REVIEW LETTERS 2024; 132:030401. [PMID: 38307063 DOI: 10.1103/physrevlett.132.030401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 12/19/2023] [Indexed: 02/04/2024]
Abstract
How long does it take to entangle two distant qubits in a quantum circuit evolved by generic unitary dynamics? We show that if the time evolution is followed by measurements of all but two infinitely separated test qubits, then the entanglement between them can undergo a phase transition and become nonzero at a finite critical time t_{c}. The fidelity of teleporting a quantum state from an input qubit to an infinitely distant output qubit shows the same critical onset. Specifically, these finite-time transitions occur in short-range interacting two-dimensional random unitary circuits and in sufficiently long-range interacting one-dimensional circuits. The phase transition is understood by mapping the random continuous-time evolution to a finite-temperature thermal state of an effective spin Hamiltonian, where the inverse temperature equals the evolution time in the circuit. In this framework, the entanglement between two distant qubits at times t>t_{c} corresponds to the emergence of long-range ferromagnetic spin correlations below the critical temperature. We verify these predictions using numerical simulation of Clifford circuits and propose potential realizations in existing platforms for quantum simulation.
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Affiliation(s)
- Yimu Bao
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Maxwell Block
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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2
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Cogan D, Su ZE, Kenneth O, Gershoni D. Deterministic generation of indistinguishable photons in a cluster state. NATURE PHOTONICS 2023; 17:324-329. [PMID: 37064524 PMCID: PMC10091623 DOI: 10.1038/s41566-022-01152-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 12/19/2022] [Indexed: 06/19/2023]
Abstract
Entanglement between particles is a basic concept of quantum sciences. The ability to produce entangled particles in a controllable manner is essential for any quantum technology. Entanglement between light particles (photons) is particularly crucial for quantum communication due to light's non-interactive nature and long-lasting coherence. Resources producing entangled multiphoton cluster states will enable communication between remote quantum nodes, as the inbuilt redundancy of cluster photons allows for repeated local measurements-compensating for losses and probabilistic Bell measurements. For feasible applications, the cluster generation should be fast, deterministic and, most importantly, its photons indistinguishable, which will allow measurements and fusion of clusters by interfering photons. Here, using periodic excitation of a semiconductor quantum-dot-confined spin, we demonstrate a multi-indistinguishable photon cluster, featuring a continuously generated string of photons at deterministic gigahertz generation rates, and an optimized entanglement length of about ten photons. The indistinguishability of the photons opens up new possibilities for scaling up the cluster's dimensionality by fusion, thus building graph states suited for measurement-based photonic quantum computers and all-photonic quantum repeaters.
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Affiliation(s)
- Dan Cogan
- The Physics Department and the Solid State Institute, Technion — Israel Institute of Technology, Haifa, Israel
| | - Zu-En Su
- The Physics Department and the Solid State Institute, Technion — Israel Institute of Technology, Haifa, Israel
| | - Oded Kenneth
- The Physics Department and the Solid State Institute, Technion — Israel Institute of Technology, Haifa, Israel
| | - David Gershoni
- The Physics Department and the Solid State Institute, Technion — Israel Institute of Technology, Haifa, Israel
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3
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Wang Z, Bao Z, Wu Y, Li Y, Cai W, Wang W, Ma Y, Cai T, Han X, Wang J, Song Y, Sun L, Zhang H, Duan L. A flying Schrödinger's cat in multipartite entangled states. SCIENCE ADVANCES 2022; 8:eabn1778. [PMID: 35275710 PMCID: PMC8916730 DOI: 10.1126/sciadv.abn1778] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 01/19/2022] [Indexed: 06/14/2023]
Abstract
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here, we present a highly scalable approach to deterministically create flying multipartite Schrödinger's cat states by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We perform full quantum state tomography on the cat states with up to four photonic modes and confirm the existence of quantum entanglement among them. We also witness the hybrid entanglement between discrete-variable states (the qubit) and continuous-variable states (the flying multipartite cat) through a joint quantum state tomography. Our work provides an enabling step for implementing a series of quantum metrology and quantum information processing protocols based on cat states.
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4
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Kovalenko O, Usenko VC, Filip R. Cross talk compensation in multimode continuous-variable entanglement distribution. OPTICS EXPRESS 2021; 29:24083-24101. [PMID: 34614660 DOI: 10.1364/oe.428628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2021] [Accepted: 06/20/2021] [Indexed: 06/13/2023]
Abstract
Two-mode squeezed states are scalable and robust entanglement resources for continuous-variable and hybrid quantum information protocols that are realized at a distance. We consider the effect of a linear cross talk in the multimode distribution of two-mode squeezed states propagating through parallel similar channels. First, to reduce degradation of the distributed Gaussian entanglement, we show that the initial two-mode squeezing entering the channel should be optimized already in the presence of a small cross talk. Second, we suggest simultaneous optimization of relative phase between the modes and their linear coupling on a receiver side prior to the use of entanglement, which can fully compensate the cross talk once the channel transmittance is the same for all the modes. For the realistic channels with similar transmittance values for either of the modes, the cross talk can be still largely compensated. This method relying on the mode interference overcomes an alternative method of entanglement localization in one pair of modes using measurement on another pair and feed-forward control. Our theoretical results pave the way to more efficient use of multimode continuous-variable photonic entanglement in scalable quantum networks with cross talk.
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5
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Lin W, Xu YL, Liu ZQ, Wang CY, Kong XM. Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:345802. [PMID: 34111860 DOI: 10.1088/1361-648x/ac0a19] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 06/10/2021] [Indexed: 06/12/2023]
Abstract
Quantum entanglement and correlations in the spin-1 Heisenberg chain with single-ion anisotropy are investigated using the quantum renormalization group method. Negativity and quantum discord (QD) are calculated with various anisotropy parameters △ and single-ion anisotropy parametersD. We focus on the relations between two abovementioned physical quantities and on transitions between the Néel, Haldane, and large-Dphases. It is found that both negativity and QD exhibit step-like patterns in different phases as the size of the system increases. Interestingly, the single-ion anisotropy parameterD, which can be modulated using nuclear electric resonance (2020Nature579205), plays an important role in tuning the quantum phase transition (QPT) of the system. Both the first partial derivative of the negativity and QD with respect toDor △ exhibit nonanalytic behavior at the phase transition points, which corresponds directly to the divergence of the correlation length. The quantum correlation critical exponents derived from negativity and QD are equal, and are the reciprocal of the correlation length exponent at each critical point. This work extends the application of quantum entanglement and correlations as tools for depicting QPTs in spin-1 systems.
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Affiliation(s)
- Wanxing Lin
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, People's Republic of China
- College of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China
| | - Yu-Liang Xu
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, People's Republic of China
- College of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China
| | - Zhong-Qiang Liu
- College of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China
| | - Chun-Yang Wang
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, People's Republic of China
- College of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China
| | - Xiang-Mu Kong
- School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, People's Republic of China
- College of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China
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6
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Daniel AK, Miyake A. Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order. PHYSICAL REVIEW LETTERS 2021; 126:090505. [PMID: 33750162 DOI: 10.1103/physrevlett.126.090505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 01/22/2021] [Indexed: 06/12/2023]
Abstract
Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between limited computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.
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Affiliation(s)
- Austin K Daniel
- Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Akimasa Miyake
- Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
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7
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Besse JC, Reuer K, Collodo MC, Wulff A, Wernli L, Copetudo A, Malz D, Magnard P, Akin A, Gabureac M, Norris GJ, Cirac JI, Wallraff A, Eichler C. Realizing a deterministic source of multipartite-entangled photonic qubits. Nat Commun 2020; 11:4877. [PMID: 32985501 PMCID: PMC7522291 DOI: 10.1038/s41467-020-18635-x] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 09/04/2020] [Indexed: 11/23/2022] Open
Abstract
Sources of entangled electromagnetic radiation are a cornerstone in quantum information processing and offer unique opportunities for the study of quantum many-body physics in a controlled experimental setting. Generation of multi-mode entangled states of radiation with a large entanglement length, that is neither probabilistic nor restricted to generate specific types of states, remains challenging. Here, we demonstrate the fully deterministic generation of purely photonic entangled states such as the cluster, GHZ, and W state by sequentially emitting microwave photons from a controlled auxiliary system into a waveguide. We tomographically reconstruct the entire quantum many-body state for up to N = 4 photonic modes and infer the quantum state for even larger N from process tomography. We estimate that localizable entanglement persists over a distance of approximately ten photonic qubits.
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Affiliation(s)
| | - Kevin Reuer
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | | | - Arne Wulff
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Lucien Wernli
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Adrian Copetudo
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Daniel Malz
- Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, Garching, 85748, Germany
- Munich Center for Quantum Science and Technology, Schellingstrasse 4, München, 80799, Germany
| | - Paul Magnard
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Abdulkadir Akin
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Mihai Gabureac
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - Graham J Norris
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
| | - J Ignacio Cirac
- Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, Garching, 85748, Germany
- Munich Center for Quantum Science and Technology, Schellingstrasse 4, München, 80799, Germany
| | - Andreas Wallraff
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
- Quantum Center, ETH Zurich, Zurich, CH-8093, Switzerland
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8
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Barasiński A, Černoch A, Lemr K. Demonstration of Controlled Quantum Teleportation for Discrete Variables on Linear Optical Devices. PHYSICAL REVIEW LETTERS 2019; 122:170501. [PMID: 31107073 DOI: 10.1103/physrevlett.122.170501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/09/2023]
Abstract
We report an experimental implementation of tripartite controlled quantum teleportation on quantum optical devices. The protocol is performed through bi- and tripartite entangled channels of discrete variables and qubits encoded in the polarization of individual photons. The experimental results demonstrate successful controlled quantum teleportation with a fidelity around 83%, well above the classical limit. By realizing the controlled quantum teleportation through a biseparable state, we show that tripartite entanglement is not a necessary resource for controlled quantum teleportation, and the controller's capability to allow or prohibit the teleportation cannot be considered to be a manifestation of tripartite entanglement. These results open new possibilities for further application of controlled quantum teleportation by lowering the teleportation channel's requirements.
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Affiliation(s)
- Artur Barasiński
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
- Institute of Physics, University of Zielona Góra, Z. Szafrana 4a, 65-516 Zielona Góra, Poland
| | - Antonín Černoch
- Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, 17. listopadu 50A, 772 07 Olomouc, Czech Republic
| | - Karel Lemr
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
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9
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Gabbrielli M, Smerzi A, Pezzè L. Multipartite Entanglement at Finite Temperature. Sci Rep 2018; 8:15663. [PMID: 30353077 PMCID: PMC6199326 DOI: 10.1038/s41598-018-31761-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Accepted: 08/17/2018] [Indexed: 11/10/2022] Open
Abstract
The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the universal phase diagram of the quantum Fisher information at a quantum phase transition. Different regions in the diagram are identified by characteristic scaling laws of the quantum Fisher information with respect to temperature. This feature has immediate consequences on the thermal robustness of quantum coherence and multipartite entanglement. We support the theoretical predictions with the analysis of paradigmatic spin systems showing symmetry-breaking quantum phase transitions and free-fermion models characterized by topological phases. In particular we show that topological systems are characterized by the survival of large multipartite entanglement, reaching the Heisenberg limit at finite temperature.
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Affiliation(s)
- Marco Gabbrielli
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy.
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10
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Barasiński A, Arkhipov II, Svozilík J. Localizable entanglement as a necessary resource of controlled quantum teleportation. Sci Rep 2018; 8:15209. [PMID: 30315175 PMCID: PMC6185991 DOI: 10.1038/s41598-018-33185-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Accepted: 09/24/2018] [Indexed: 11/08/2022] Open
Abstract
We analyze the controlled teleportation protocol through three-qubit mixed states. In particular, we investigate the relation between the faithfulness of the controlled teleportation scheme and entanglement. While our knowledge concerning controlled teleportation and entanglement in pure states is well established, for mixed states it is considerably much harder task and very little has been done in this field. Here, we present counterintuitive results that provide a new light on controlled teleportation protocol. It is shown that even mixed biseparable states are useful for this protocol along with genuine entangled three-qubit states.
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Affiliation(s)
- Artur Barasiński
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46, Olomouc, Czech Republic.
- Institute of Physics, University of Zielona Góra, Z. Szafrana 4a, 65-516, Zielona Góra, Poland.
| | - Ievgen I Arkhipov
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46, Olomouc, Czech Republic
| | - Jiří Svozilík
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46, Olomouc, Czech Republic
- Quantum Optics Laboratory, Universidad de los Andes, A.A. 4976, Bogotá, D.C., Colombia
- Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, 76230, Juriquilla, Querétaro, Mexico
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11
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De Chiara G, Sanpera A. Genuine quantum correlations in quantum many-body systems: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074002. [PMID: 29671752 DOI: 10.1088/1361-6633/aabf61] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
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Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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12
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Bera A, Das T, Sadhukhan D, Singha Roy S, Sen De A, Sen U. Quantum discord and its allies: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:024001. [PMID: 28824014 DOI: 10.1088/1361-6633/aa872f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.
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Affiliation(s)
- Anindita Bera
- Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India. Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India
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13
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Pezzè L, Gabbrielli M, Lepori L, Smerzi A. Multipartite Entanglement in Topological Quantum Phases. PHYSICAL REVIEW LETTERS 2017; 119:250401. [PMID: 29303346 DOI: 10.1103/physrevlett.119.250401] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Indexed: 06/07/2023]
Abstract
We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.
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Affiliation(s)
- Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Marco Gabbrielli
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Luca Lepori
- Dipartimento di Scienze Fisiche e Chimiche, Università dell'Aquila, via Vetoio 42, I-67010 Coppito-L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, I-67100 Assergi (AQ), Italy
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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14
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Abstract
We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J = ∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should be taken into account in the approximations starting from a mean-field limit.
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Affiliation(s)
- Konstantin V Krutitsky
- Institut für Theoretische Physik, Universität Duisburg-Essen, D-47048, Duisburg, Germany.
| | - Andreas Osterloh
- Institut für Theoretische Physik, Universität Duisburg-Essen, D-47048, Duisburg, Germany
| | - Ralf Schützhold
- Institut für Theoretische Physik, Universität Duisburg-Essen, D-47048, Duisburg, Germany
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15
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Mičuda M, Koutný D, Miková M, Straka I, Ježek M, Mišta L. Experimental demonstration of a fully inseparable quantum state with nonlocalizable entanglement. Sci Rep 2017; 7:45045. [PMID: 28344336 PMCID: PMC5366861 DOI: 10.1038/srep45045] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 02/20/2017] [Indexed: 11/09/2022] Open
Abstract
Localizability of entanglement in fully inseparable states is a key ingredient of assisted quantum information protocols as well as measurement-based models of quantum computing. We investigate the existence of fully inseparable states with nonlocalizable entanglement, that is, with entanglement which cannot be localized between any pair of subsystems by any measurement on the remaining part of the system. It is shown, that the nonlocalizable entanglement occurs already in suitable mixtures of a three-qubit GHZ state and white noise. Further, we generalize this set of states to a two-parametric family of fully inseparable three-qubit states with nonlocalizable entanglement. Finally, we demonstrate experimentally the existence of nonlocalizable entanglement by preparing and characterizing one state from the family using correlated single photons and linear optical circuit.
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Affiliation(s)
- M Mičuda
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - D Koutný
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M Miková
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - I Straka
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M Ježek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - L Mišta
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
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16
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Cheng WW, Wang XY, Sheng YB, Gong LY, Zhao SM, Liu JM. Finite-temperature scaling of trace distance discord near criticality in spin diamond structure. Sci Rep 2017; 7:42360. [PMID: 28198404 PMCID: PMC5309762 DOI: 10.1038/srep42360] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Accepted: 01/08/2017] [Indexed: 11/09/2022] Open
Abstract
In this work we explore the quantum correlation quantified by trace distance discord as a measure to analyze the quantum critical behaviors in the Ising-XXZ diamond structure at finite temperatures. It is found that the first-order derivative of the trace distance discord exhibits a maximum around the critical point at finite temperatures. By analyzing the finite-temperature scaling behavior, we show that such a quantum correlation can detect exactly the quantum phase transitions from the entan-gled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. The results also indicate that the above two kinds of transitions can be distinguished by the different finite-temperature scaling behaviors. Moreover, we find that the trace distance discord, in contrast to other typical quantum correlations (e.g., concurrence, quantum discord and Hellinger distance), may be more reliable to exactly spotlight the critical points of this model at finite temperatures under certain situations.
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Affiliation(s)
- W W Cheng
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - X Y Wang
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - Y B Sheng
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - L Y Gong
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China.,National Laboratory of Solid State Microstructures &Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - S M Zhao
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - J M Liu
- National Laboratory of Solid State Microstructures &Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
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17
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Schwartz I, Cogan D, Schmidgall ER, Don Y, Gantz L, Kenneth O, Lindner NH, Gershoni D. Deterministic generation of a cluster state of entangled photons. Science 2016; 354:434-437. [DOI: 10.1126/science.aah4758] [Citation(s) in RCA: 194] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Accepted: 08/30/2016] [Indexed: 11/02/2022]
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18
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Chitambar E, Streltsov A, Rana S, Bera MN, Adesso G, Lewenstein M. Assisted Distillation of Quantum Coherence. PHYSICAL REVIEW LETTERS 2016; 116:070402. [PMID: 26943512 DOI: 10.1103/physrevlett.116.070402] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2015] [Indexed: 06/05/2023]
Abstract
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.
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Affiliation(s)
- E Chitambar
- Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901, USA
| | - A Streltsov
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
| | - S Rana
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
| | - M N Bera
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
| | - G Adesso
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, E-08010 Barcelona, Spain
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19
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Sadhukhan D, Roy SS, Rakshit D, Prabhu R, Sen De A, Sen U. Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain. Phys Rev E 2016; 93:012131. [PMID: 26871048 DOI: 10.1103/physreve.93.012131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 06/05/2023]
Abstract
Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.
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Affiliation(s)
- Debasis Sadhukhan
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Sudipto Singha Roy
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Debraj Rakshit
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - R Prabhu
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Aditi Sen De
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Ujjwal Sen
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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20
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Schwaiger K, Sauerwein D, Cuquet M, de Vicente JI, Kraus B. Operational Multipartite Entanglement Measures. PHYSICAL REVIEW LETTERS 2015; 115:150502. [PMID: 26550713 DOI: 10.1103/physrevlett.115.150502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2015] [Indexed: 06/05/2023]
Abstract
We introduce two operational entanglement measures that are applicable for arbitrary multipartite (pure or mixed) states. One of them characterizes the potentiality of a state to generate other states via local operations assisted by classical communication and the other characterizes the simplicity of generating the state at hand. We show how these measures can be generalized to two classes of entanglement measures. Moreover, we compute the new measures for pure few-partite systems and use them to characterize the entanglement contained in a three-qubit state. We identify the Greenberger-Horne-Zeilinger and W state as the most powerful pure three-qubit states regarding state manipulation.
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Affiliation(s)
- K Schwaiger
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - D Sauerwein
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - M Cuquet
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - J I de Vicente
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés (Madrid) E-28911, Spain
| | - B Kraus
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
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21
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Hemmatiyan S, Rahimi Movassagh M, Ghassemi N, Kargarian M, Rezakhani AT, Langari A. Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:155601. [PMID: 25812634 DOI: 10.1088/0953-8984/27/15/155601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the 'perturbative continuous unitary transformations' approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
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Affiliation(s)
- S Hemmatiyan
- Department of Physics, Texas A&M University, College Station, TX 77843-4242, USA. Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
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22
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Orieux A, D'Arrigo A, Ferranti G, Franco RL, Benenti G, Paladino E, Falci G, Sciarrino F, Mataloni P. Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics. Sci Rep 2015; 5:8575. [PMID: 25712406 PMCID: PMC4339803 DOI: 10.1038/srep08575] [Citation(s) in RCA: 125] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2014] [Accepted: 01/26/2015] [Indexed: 11/09/2022] Open
Abstract
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely local operation, without acquiring any information on the environment; then, we use a closed-loop scheme in which the environment is measured, the outcome controling the local operations on the system. The restored entanglement is a manifestation of "hidden" quantum correlations resumed by the local control. Relying on local control, both schemes improve the efficiency of entanglement sharing in distributed quantum networks.
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Affiliation(s)
- Adeline Orieux
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, I-00185 Roma, Italy
| | - Antonio D'Arrigo
- CNR-IMM UOS Università (MATIS), Consiglio Nazionale delle Ricerche, Via Santa Sofia 64, 95123 Catania, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania, Italy
| | - Giacomo Ferranti
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, I-00185 Roma, Italy
| | - Rosario Lo Franco
- Dipartimento di Fisica e Chimica, Università di Palermo, via Archirafi 36, 90123 Palermo, Italy
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
| | - Elisabetta Paladino
- CNR-IMM UOS Università (MATIS), Consiglio Nazionale delle Ricerche, Via Santa Sofia 64, 95123 Catania, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, 95123 Catania, Italy
| | - Giuseppe Falci
- CNR-IMM UOS Università (MATIS), Consiglio Nazionale delle Ricerche, Via Santa Sofia 64, 95123 Catania, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi Catania, Via Santa Sofia 64, 95123 Catania, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, 95123 Catania, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, I-00185 Roma, Italy
| | - Paolo Mataloni
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, I-00185 Roma, Italy
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23
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Factorization and Criticality in the Anisotropic XY Chain via Correlations. ENTROPY 2015. [DOI: 10.3390/e17020790] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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24
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Dhar HS, Sen De A, Sen U. Characterizing genuine multisite entanglement in isotropic spin lattices. PHYSICAL REVIEW LETTERS 2013; 111:070501. [PMID: 23992053 DOI: 10.1103/physrevlett.111.070501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2012] [Indexed: 06/02/2023]
Abstract
We consider a class of large superposed states, obtained from dimer coverings on spin-1/2 isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty entangled, irrespective of the geometry and dimension of the isotropic lattice. We then present an efficient method to characterize the genuine multisite entanglement in the case of isotropic square spin-1/2 lattices, with short-range dimer coverings. We use this iterative analytical method to calculate the multisite entanglement of finite-sized lattices, which through finite-size scaling, enables us to obtain the estimate of the multisite entanglement of the infinite square lattice. The method can be a useful tool to investigate other single- and multisite properties of such states.
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25
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Chuan TK, Maillard J, Modi K, Paterek T, Paternostro M, Piani M. Quantum discord bounds the amount of distributed entanglement. PHYSICAL REVIEW LETTERS 2012; 109:070501. [PMID: 23006347 DOI: 10.1103/physrevlett.109.070501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2012] [Indexed: 06/01/2023]
Abstract
The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.
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Affiliation(s)
- T K Chuan
- Centre for Quantum Technologies, National University of Singapore, Singapore
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26
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de Vicente JI, Carle T, Streitberger C, Kraus B. Complete set of operational measures for the characterization of three-qubit entanglement. PHYSICAL REVIEW LETTERS 2012; 108:060501. [PMID: 22401041 DOI: 10.1103/physrevlett.108.060501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Indexed: 05/31/2023]
Abstract
We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end, we derive a new decomposition for arbitrary three-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.
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Affiliation(s)
- J I de Vicente
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
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27
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Kraus B. Local unitary equivalence of multipartite pure states. PHYSICAL REVIEW LETTERS 2010; 104:020504. [PMID: 20366579 DOI: 10.1103/physrevlett.104.020504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2009] [Indexed: 05/29/2023]
Abstract
Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under local unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU equivalent iff their standard forms coincide. The LU-equivalence problem for nongeneric states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.
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Affiliation(s)
- B Kraus
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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28
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Ding L, Bray-Ali N, Yu R, Haas S. Subarea law of entanglement in nodal fermionic systems. PHYSICAL REVIEW LETTERS 2008; 100:215701. [PMID: 18518619 DOI: 10.1103/physrevlett.100.215701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2008] [Revised: 04/22/2008] [Indexed: 05/26/2023]
Abstract
We investigate the subarea-law scaling behavior of the block entropy in bipartite fermionic systems which do not have a finite Fermi surface. It is found that in gapped regimes the leading subarea term is a negative constant, whereas in critical regimes with point nodes the leading subarea law is a logarithmic additive term. At the phase boundary that separates the critical and noncritical regimes, the subarea scaling shows power-law behavior.
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Affiliation(s)
- Letian Ding
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
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29
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Cubitt TS, Cirac JI. Engineering correlation and entanglement dynamics in spin systems. PHYSICAL REVIEW LETTERS 2008; 100:180406. [PMID: 18518356 DOI: 10.1103/physrevlett.100.180406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2007] [Indexed: 05/26/2023]
Abstract
We show that correlation and entanglement dynamics of spin systems can be precisely controlled and engineered using only a small number of external physical control parameters. We first point out that the correlation dynamics of such systems can be understood in terms of spin-wave propagation, giving a simple physical explanation of the behavior seen in a number of recent works. We then extend this picture to more realistic translationally invariant systems prepared in product states. Since spin waves propagate according to a system's dispersion relation which typically depends on external physical parameters, this insight provides a convenient way to understand how dynamics can be controlled. We demonstrate these ideas in a simple example system, showing that correlations can be made to propagate in well-defined packets whose speed can be engineered in advance, controlled during the evolution, or even stopped altogether.
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Affiliation(s)
- T S Cubitt
- Max Planck Institut für Quantenoptik, Hans-Kopfermann Strasse 1, D-85748 Garching, Germany
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30
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Boixo S, Monras A. Operational interpretation for global multipartite entanglement. PHYSICAL REVIEW LETTERS 2008; 100:100503. [PMID: 18352168 DOI: 10.1103/physrevlett.100.100503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Indexed: 05/26/2023]
Abstract
We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.
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Affiliation(s)
- S Boixo
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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31
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Wolf MM, Verstraete F, Hastings MB, Cirac JI. Area laws in quantum systems: mutual information and correlations. PHYSICAL REVIEW LETTERS 2008; 100:070502. [PMID: 18352531 DOI: 10.1103/physrevlett.100.070502] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2007] [Indexed: 05/26/2023]
Abstract
The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.
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Affiliation(s)
- Michael M Wolf
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, Germany
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32
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Barry JH, Muttalib KA, Tanaka T. Solutions for correlations along the coexistence curve and at the critical point of a kagomé lattice gas with three-particle interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011102. [PMID: 18351813 DOI: 10.1103/physreve.77.011102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2007] [Indexed: 05/26/2023]
Abstract
We consider a two-dimensional (d=2) kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.
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Affiliation(s)
- J H Barry
- Department of Physics, University of Florida, P.O. Box 118440, Gainesville, Florida 32611-8440, USA
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33
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Chhajlany RW, Tomczak P, Wójcik A. Topological estimator of block entanglement for Heisenberg antiferromagnets. PHYSICAL REVIEW LETTERS 2007; 99:167204. [PMID: 17995287 DOI: 10.1103/physrevlett.99.167204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2007] [Revised: 06/08/2007] [Indexed: 05/25/2023]
Abstract
We introduce a computable estimator of block entanglement entropy for many-body spin systems admitting total singlet ground states. Building on a simple geometrical interpretation of entanglement entropy of the so-called valence bond states, this estimator is defined as the average number of common singlets to two subsystems of spins. We show that our estimator possesses the characteristic scaling properties of the block entanglement entropy in critical and noncritical one-dimensional Heisenberg systems. We invoke this new measure to examine entanglement scaling in the two-dimensional Heisenberg model on a square lattice revealing an "area law" for the gapped phase and a logarithmic correction to this law in the gapless phase.
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Affiliation(s)
- Ravindra W Chhajlany
- Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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34
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Alet F, Capponi S, Laflorencie N, Mambrini M. Valence bond entanglement entropy. PHYSICAL REVIEW LETTERS 2007; 99:117204. [PMID: 17930468 DOI: 10.1103/physrevlett.99.117204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2007] [Indexed: 05/25/2023]
Abstract
We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.
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Affiliation(s)
- Fabien Alet
- Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier, CNRS, 31062 Toulouse, France.
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35
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Stone MB, Tian W, Lumsden MD, Granroth GE, Mandrus D, Chung JH, Harrison N, Nagler SE. Quantum spin correlations in an organometallic alternating-sign chain. PHYSICAL REVIEW LETTERS 2007; 99:087204. [PMID: 17930978 DOI: 10.1103/physrevlett.99.087204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2007] [Indexed: 05/25/2023]
Abstract
High resolution neutron scattering is used to study excitations in the organometallic magnet (CH3)2NH2CuCl3 (DMACuCl3). Combined with bulk magnetization and susceptibility studies, the new results imply that DMACuCl3 is a realization of the S=1/2 alternating antiferromagnetic-ferromagnetic (AFM-FM) chain. Coupled-cluster calculations indicate that the AFM and FM interactions have nearly the same strength, while analysis of scattering intensities shows evidence for interdimer spin correlations. Results are discussed in the context of recent ideas concerning quantum entanglement.
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Affiliation(s)
- M B Stone
- Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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36
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de Oliveira TR, Rigolin G, de Oliveira MC, Miranda E. Multipartite entanglement signature of quantum phase transitions. PHYSICAL REVIEW LETTERS 2006; 97:170401. [PMID: 17155445 DOI: 10.1103/physrevlett.97.170401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2006] [Indexed: 05/12/2023]
Abstract
We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.
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Affiliation(s)
- Thiago R de Oliveira
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, CEP 13083-970, Campinas, São Paulo, Brazil.
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37
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Van den Nest M, Miyake A, Dür W, Briegel HJ. Universal resources for measurement-based quantum computation. PHYSICAL REVIEW LETTERS 2006; 97:150504. [PMID: 17155309 DOI: 10.1103/physrevlett.97.150504] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2006] [Indexed: 05/12/2023]
Abstract
We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess the universality of graph states by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal nongraph state.
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Affiliation(s)
- Maarten Van den Nest
- Institut für Quantenoptik und Quanteninformation der Osterreichischen, Akademie der Wissenschaften, Innsbruck, Austria
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38
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Bravyi S, Hastings MB, Verstraete F. Lieb-Robinson bounds and the generation of correlations and topological quantum order. PHYSICAL REVIEW LETTERS 2006; 97:050401. [PMID: 17026080 DOI: 10.1103/physrevlett.97.050401] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2006] [Indexed: 05/12/2023]
Abstract
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.
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Affiliation(s)
- S Bravyi
- IBM Watson Research Center, Yorktown Heights, NY 10598, USA
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39
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40
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Campos Venuti L, Degli Esposti Boschi C, Roncaglia M. Long-distance entanglement in spin systems. PHYSICAL REVIEW LETTERS 2006; 96:247206. [PMID: 16907279 DOI: 10.1103/physrevlett.96.247206] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2006] [Indexed: 05/11/2023]
Abstract
Most quantum system with short-ranged interactions show a fast decay of entanglement with the distance. In this Letter, we focus on the peculiarity of some systems to distribute entanglement between distant parties. Even in realistic models, like the spin-1 Heisenberg chain, sizable entanglement is present between arbitrarily distant particles. We show that long-distance entanglement appears for values of the microscopic parameters which do not coincide with known quantum critical points, hence signaling a transition detected only by genuine quantum correlations.
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Affiliation(s)
- L Campos Venuti
- Dipartimento di Fisica, Università di Bologna, Viale C. Berti-Pichat 6/2, I-40127 Bologna, Italy
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41
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Quan HT, Song Z, Liu XF, Zanardi P, Sun CP. Decay of Loschmidt echo enhanced by quantum criticality. PHYSICAL REVIEW LETTERS 2006; 96:140604. [PMID: 16712060 DOI: 10.1103/physrevlett.96.140604] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2005] [Indexed: 05/09/2023]
Abstract
We study the transition of a quantum system from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modeled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply.
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Affiliation(s)
- H T Quan
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China
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42
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Oleś AM, Horsch P, Feiner LF, Khaliullin G. Spin-orbital entanglement and violation of the Goodenough-Kanamori rules. PHYSICAL REVIEW LETTERS 2006; 96:147205. [PMID: 16712118 DOI: 10.1103/physrevlett.96.147205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2005] [Indexed: 05/09/2023]
Abstract
We point out that large composite spin-orbital fluctuations in Mott insulators with t(2g) orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules.
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Affiliation(s)
- Andrzej M Oleś
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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43
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Calsamiglia J, Hartmann L, Dür W, Briegel HJ. Spin gases: quantum entanglement driven by classical kinematics. PHYSICAL REVIEW LETTERS 2005; 95:180502. [PMID: 16383883 DOI: 10.1103/physrevlett.95.180502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2005] [Indexed: 05/05/2023]
Abstract
A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.
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Affiliation(s)
- J Calsamiglia
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
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44
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Adesso G, Illuminati F. Equivalence between entanglement and the optimal fidelity of continuous variable teleportation. PHYSICAL REVIEW LETTERS 2005; 95:150503. [PMID: 16241708 DOI: 10.1103/physrevlett.95.150503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2004] [Indexed: 05/05/2023]
Abstract
We devise the optimal form of Gaussian resource states enabling continuous-variable teleportation with maximal fidelity. We show that a nonclassical optimal fidelity of N-user teleportation networks is necessary and sufficient for N-party entangled Gaussian resources, yielding an estimator of multipartite entanglement. The entanglement of teleportation is equivalent to the entanglement of formation in a two-user protocol, and to the localizable entanglement in a multiuser one. Finally, we show that the continuous-variable tangle, quantifying entanglement sharing in three-mode Gaussian states, is defined operationally in terms of the optimal fidelity of a tripartite teleportation network.
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Affiliation(s)
- Gerardo Adesso
- Dipartimento di Fisica E. R. Caianiello, Università di Salerno, CNR-Coherentia, Gruppo di Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy
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45
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46
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Venuti LC, Roncaglia M. Analytic relations between localizable entanglement and string correlations in spin systems. PHYSICAL REVIEW LETTERS 2005; 94:207207. [PMID: 16090283 DOI: 10.1103/physrevlett.94.207207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2005] [Indexed: 05/03/2023]
Abstract
We study the relation between the recently defined localizable entanglement and generalized correlations in quantum spin systems. Differently from the current belief, the localizable entanglement is always given by the average of a generalized string. Using symmetry arguments we show that in most spin-1/2 and spin-1 systems the localizable entanglement reduces to the spin-spin or string correlations, respectively. We prove that a general class of spin-1 systems, which includes the Heisenberg model, can be used as a perfect quantum channel. These conclusions are obtained in analytic form and confirm some results found previously on numerical grounds.
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Affiliation(s)
- L Campos Venuti
- Dipartimento di Fisica, V.le C. Berti-Pichat 6/2, I-40127 Bologna, Italy
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47
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Dür W, Hartmann L, Hein M, Lewenstein M, Briegel HJ. Entanglement in spin chains and lattices with long-range Ising-type interactions. PHYSICAL REVIEW LETTERS 2005; 94:097203. [PMID: 15783996 DOI: 10.1103/physrevlett.94.097203] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2004] [Indexed: 05/24/2023]
Abstract
We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long-range Ising-type interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N-->infinity. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates and determine S(L) analytically for special configurations. We find an unbounded increase of S(L) as well as diverging correlation and entanglement length under certain circumstances. For arbitrarily large N, we can efficiently calculate all quantities associated with reduced density operators of up to ten particles.
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Affiliation(s)
- W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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48
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Wu LA, Sarandy MS, Lidar DA. Quantum phase transitions and bipartite entanglement. PHYSICAL REVIEW LETTERS 2004; 93:250404. [PMID: 15697878 DOI: 10.1103/physrevlett.93.250404] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2004] [Indexed: 05/24/2023]
Abstract
We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.
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Affiliation(s)
- L-A Wu
- Chemical Physics Theory Group, Department of Chemistry, Center for Quantum Information and Quantum Control, University of Toronto, Ontario M5S 3H6, Canada
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49
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Verstraete F, Porras D, Cirac JI. Density matrix renormalization group and periodic boundary conditions: a quantum information perspective. PHYSICAL REVIEW LETTERS 2004; 93:227205. [PMID: 15601115 DOI: 10.1103/physrevlett.93.227205] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2004] [Indexed: 05/24/2023]
Abstract
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads to a variational formulation of DMRG which allows for dramatic improvements in the case of problems with periodic boundary conditions. The picture also explains some features of the method in terms of entanglement and teleportation.
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Affiliation(s)
- F Verstraete
- Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748, Germany
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50
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Roscilde T, Verrucchi P, Fubini A, Haas S, Tognetti V. Studying quantum spin systems through entanglement estimators. PHYSICAL REVIEW LETTERS 2004; 93:167203. [PMID: 15525026 DOI: 10.1103/physrevlett.93.167203] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2004] [Indexed: 05/24/2023]
Abstract
We study the field dependence of the entanglement of formation in anisotropic S=1/2 antiferromagnetic chains displaying a T=0 field-driven quantum phase transition. The analysis is carried out via quantum Monte Carlo simulations. At zero temperature the entanglement estimators show abrupt changes at and around criticality, vanishing below the critical field, in correspondence with an exactly factorized state, and then immediately recovering a finite value upon passing through the quantum phase transition. At the quantum-critical point, a deep minimum in the pairwise-to-global entanglement ratio shows that multispin entanglement is strongly enhanced; moreover this signature represents a novel way of detecting the quantum phase transition of the system, relying entirely on entanglement estimators.
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Affiliation(s)
- Tommaso Roscilde
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484, USA
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