1
|
Cesário AT, Ferreira DLB, Debarba T, Iemini F, Maciel TO, Vianna RO. Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1161. [PMID: 36010825 PMCID: PMC9407496 DOI: 10.3390/e24081161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 07/20/2022] [Accepted: 07/23/2022] [Indexed: 06/15/2023]
Abstract
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order-disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the 1D-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-1/2 chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique.
Collapse
Affiliation(s)
- André T. Cesário
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
| | - Diego L. B. Ferreira
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
| | - Tiago Debarba
- Departamento Acadêmico de Ciências da Natureza, Universidade Tecnológica Federal do Paraná (UTFPR), Campus Cornélio Procópio, Avenida Alberto Carazzai 1640, Cornélio Procópio 86300-000, Brazil
| | - Fernando Iemini
- Instituto de Física, Universidade Federal Fluminense (UFF), Niterói 24210-346, Brazil
| | - Thiago O. Maciel
- Instituto de Física, Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro 21941-972, Brazil
| | - Reinaldo O. Vianna
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil
| |
Collapse
|
2
|
Chen T, Cheng YC. Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems. J Chem Phys 2022; 157:064106. [PMID: 35963728 DOI: 10.1063/5.0099761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system + bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long range interaction systems.
Collapse
Affiliation(s)
- Tyler Chen
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
| | - Yu-Chen Cheng
- Department of Data Science, Dana-Farber Cancer Institute, Boston, Massachusetts 02215, USA
| |
Collapse
|
3
|
Japaridze GI, Cheraghi H, Mahdavifar S. Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction. Phys Rev E 2021; 104:014134. [PMID: 34412371 DOI: 10.1103/physreve.104.014134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 06/29/2021] [Indexed: 11/07/2022]
Abstract
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.
Collapse
Affiliation(s)
- G I Japaridze
- Center for Condensed Matter Theory and Quantum Computations Ilia State University, Tbilisi, Georgia
| | - Hadi Cheraghi
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
| | - Saeed Mahdavifar
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
| |
Collapse
|
4
|
Radhakrishnan C, Laurière M, Byrnes T. Multipartite Generalization of Quantum Discord. PHYSICAL REVIEW LETTERS 2020; 124:110401. [PMID: 32242682 DOI: 10.1103/physrevlett.124.110401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Revised: 02/12/2020] [Accepted: 02/12/2020] [Indexed: 06/11/2023]
Abstract
A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.
Collapse
Affiliation(s)
- Chandrashekar Radhakrishnan
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Laboratoire Systèmes Complexes et Information Quantique, ESIEA Group, 9 Rue Vèsale, Paris 75005, France
| | - Mathieu Laurière
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- Princeton University, ORFE Department, 98 Charlton Street, Princeton, New Jersey 08540, USA
| | - Tim Byrnes
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
- Department of Physics, New York University, New York, New York 10003, USA
| |
Collapse
|
5
|
Zad HA, Ananikian N, Kenna R. The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:445802. [PMID: 31379354 DOI: 10.1088/1361-648x/ab3136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Studies of the structural effects on the thermodynamic properties of two types of Ising-Heisenberg ladders are comprehensively reported. Each structure comprises spin-1/2 particles partitioned into adjoined blocks or cages formed from butterfly-shaped plaquettes and interacting in an Ising manner. We use the transfer-matrix approach to determine the partition functions of these models and numerically investigate their magnetization and specific-heat properties. Both models illustrate all characteristic features of low-temperature magnetization processes and thermodynamics properties such as abrupt variations of the magnetization curves, Schottky-type peak and a double-peak structure of the specific heat. Comparisons between the two ladders reveal some differences in their magnetic and thermodynamic behaviors. For instance, difference in the number of intermediate magnetization plateaus, also difference in the height and temperature-position of the specific heat peaks. We also present that the fluctuations of the specific heat with respect to the magnetic field are in highly accordance with the magnetization plateaus and magnetization jumps. Moreover, we find quite interesting threshold reentrance points within the matrix-plot of the specific heat shown in the (T/J - B/J) plane, at which the temperature-position of the Schottky peak alternatively change. Finally, we prove that the reentrance points can be satisfactorily considered as magnetization plateau witnesses even in the high temperatures.
Collapse
Affiliation(s)
- Hamid Arian Zad
- Alikhanyan National Science Laboratory, Alikhanian Br. 2, 0036 Yerevan, Armenia. ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | | | | |
Collapse
|
6
|
Tan XD, Kang XB, Zhao LM, Zhang JJ, Hao HS. Quantum dissonance in chiral graphene nanoribbons. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:205602. [PMID: 30763919 DOI: 10.1088/1361-648x/ab071c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Based on the effective spin-ladder model, we study the properties of quantum dissonance (Q) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T, and discuss the influences of relative location between two edge spins, ribbon width, temperature, and on-site Coulomb repulsion (U) on Q. The results show that Q is widely present in Wannier edge states. For intra-edge coupled spin pairs, quantum entanglement (E) is zero, but there still exists considerable value of Q. Interestingly, Q always keeps a constant for entangled edge spin pairs. Considering the thermal effect, it shows that Q always decays with the increasing temperature T, and the decay rate is very sensitive to the intensity of U. Compared Q with E and total quantum correlation (quantum discord, denoted by D), we conjecture that the quantum correlations for a bipartite Wannier edge state in CGNRs satisfy the relation Q ⩽ D-E.
Collapse
Affiliation(s)
- Xiao-Dong Tan
- School of Science, Henan Institute of Engineering, Zhengzhou 451191, People's Republic of China
| | | | | | | | | |
Collapse
|
7
|
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: 12] [Impact Index Per Article: 2.0] [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.
Collapse
Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | | |
Collapse
|
8
|
Arian Zad H, Ananikian N. Phase transitions and magnetization of the mixed-spin Ising-Heisenberg double sawtooth frustrated ladder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:165403. [PMID: 29589591 DOI: 10.1088/1361-648x/aab644] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
The mixed spin-(1,1/2) Ising-Heisenberg double sawtooth ladder containing a mixture of both spin-1 and spin-1/2 nodal atoms, and the spin-1/2 interstitial dimers are approximately solved by the transfer-matrix method. Here, we study in detail the ground-state phase diagrams, also influences of the bilinear exchange coupling on the rungs and cyclic four-spin exchange interaction in square plaquette of each block on the magnetization and magnetic susceptibility of the suggested ladder at low temperature. Such a double sawtooth ladder may be found in a Shastry-Sutherland lattice-type. In spite of the spin ordering of odd and even blocks being different from each other, due to the commutation relation between all different block Hamiltonians, phase diagrams, magnetization behavior and thermodynamic properties of the model are the same for odd and even blocks. We show that at low temperature, both exchange couplings can change the quality and quantity of the magnetization plateaus versus the magnetic field changes. Specially, we find a new magnetization plateau [Formula: see text] for this model. Besides, we examine the magnetic susceptibility and specific heat of the model in detail. It is proven that behaviors of the magnetization and the magnetic susceptibility coincide at low temperature. The specific heat displays diverse temperature dependencies, which include a Schottky-type peak at a special temperature interval. We observe that with increase of the bilinear exchange coupling on the rungs, second peak temperature dependence grows.
Collapse
Affiliation(s)
- Hamid Arian Zad
- Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
| | | |
Collapse
|
9
|
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.
Collapse
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
| | | | | | | | | | | |
Collapse
|
10
|
Arian Zad H, Ananikian N. Phase transitions and thermal entanglement of the distorted Ising-Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:455402. [PMID: 29049024 DOI: 10.1088/1361-648x/aa8dd0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.
Collapse
Affiliation(s)
- Hamid Arian Zad
- Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
| | | |
Collapse
|
11
|
Revealing Tripartite Quantum Discord with Tripartite Information Diagram. ENTROPY 2017. [DOI: 10.3390/e19110602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
12
|
Sudden Transition between Classical to Quantum Decoherence in bipartite correlated Qutrit Systems. Sci Rep 2017; 7:44654. [PMID: 28317916 PMCID: PMC5357944 DOI: 10.1038/srep44654] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Accepted: 02/13/2017] [Indexed: 11/08/2022] Open
Abstract
Classical to quantum decoherence transition, an issue existing for incoherent superposition of Bell-diagonal states is studied for three dimensional bipartite AB mixed quantum systems. Depending on the initial conditions, the dynamics of classical and quantum correlations can exhibit a sudden transition between classical to quantum decoherence. This result is calculated numerically by using entropic and geometric measures of correlations. An alternative explanation for this effect could be obtained by extending the bipartite A ⊗ B qutrit system to a pure tripartite A ⊗ B ⊗ C system. The freezing of classical correlations in AB is related to a freezing of the entanglement in the AC bipartition.
Collapse
|
13
|
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.
Collapse
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
| |
Collapse
|
14
|
Tan XD, Koop C, Liao XP, Sun L. Quantum correlations in chiral graphene nanoribbons. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:435601. [PMID: 27603682 DOI: 10.1088/0953-8984/28/43/435601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We compute the entanglement and the quantum discord (QD) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T (canonical ensemble). We show that the entanglement only exists in inter-edge coupled spin pairs, and there is no entanglement between any two spins at the same ribbon edge. By contrast, almost all edge spin pairs can hold non-zero QD, which strongly depends on the ribbon width and the Coulomb repulsion among electrons. More intriguingly, the dominant entanglement always occurs in the pair of nearest abreast spins across the ribbon, and even at room temperature this type of entanglement is still very robust, especially for narrow CGNRs with the weak Coulomb repulsion. These remarkable properties make CGNRs very promising for possible applications in spin-quantum devices.
Collapse
Affiliation(s)
- Xiao-Dong Tan
- SEU-FEI Nano-Pico Center, Key Laboratory of MEMS of Ministry of Education, Collaborative Innovation Center for Micro/Nano Fabrication, Device and System, Southeast University, Nanjing 210096, People's Republic of China
| | | | | | | |
Collapse
|
15
|
Abstract
We study the connections between local quantum coherence (LQC) based on Wigner-Yanase skew information and quantum phase transitions (QPTs). When applied on the one-dimensional Hubbard, XY spin chain with three-spin interaction, and Su-Schrieffer-Heeger models, the LQC and its derivatives are used successfully to detect different types of QPTs in these spin and fermionic systems. Furthermore, the LQC is effective as the quantum discord (QD) in detecting QPTs at finite temperatures, where the entanglement has lost its effectiveness. We also demonstrate that the LQC can exhibit different behaviors in many forms compared with the QD.
Collapse
|
16
|
Universal quantum correlation close to quantum critical phenomena. Sci Rep 2016; 6:26042. [PMID: 27189504 PMCID: PMC4870697 DOI: 10.1038/srep26042] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Accepted: 04/26/2016] [Indexed: 12/03/2022] Open
Abstract
We study the ground state quantum correlation of Ising model in a transverse field (ITF) by implementing the quantum renormalization group (QRG) theory. It is shown that various quantum correlation measures and the Clauser-Horne-Shimony-Holt inequality will highlight the critical point related with quantum phase transitions, and demonstrate nonanalytic phenomena and scaling behavior when the size of the systems becomes large. Our results also indicate a universal behavior of the critical exponent of ITF under QRG theory that the critical exponent of different measures is identical, even when the quantities vary from entanglement measures to quantum correlation measures. This means that the two kinds of quantum correlation criterion including the entanglement-separability paradigm and the information-theoretic paradigm have some connections between them. These remarkable behaviors may have important implications on condensed matter physics because the critical exponent directly associates with the correlation length exponent.
Collapse
|
17
|
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]
|
18
|
Li J, Yu T, Lin HQ, You JQ. Probing the non-locality of Majorana fermions via quantum correlations. Sci Rep 2014; 4:4930. [PMID: 24816484 PMCID: PMC4017219 DOI: 10.1038/srep04930] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Accepted: 04/23/2014] [Indexed: 11/27/2022] Open
Abstract
Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.
Collapse
Affiliation(s)
- Jun Li
- 1] Beijing Computational Science Research Center, Beijing 100084, China [2] College of Physics and Electronic Engineering, Dezhou University, Dezhou 253023, China
| | - Ting Yu
- Center for Controlled Quantum Systems and Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
| | - Hai-Qing Lin
- Beijing Computational Science Research Center, Beijing 100084, China
| | - J Q You
- Beijing Computational Science Research Center, Beijing 100084, China
| |
Collapse
|
19
|
Eremeev V, Ciobanu N, Orszag M. Thermal effects on sudden changes and freezing of correlations between remote atoms in a cavity quantum electrodynamics network. OPTICS LETTERS 2014; 39:2668-2671. [PMID: 24784073 DOI: 10.1364/ol.39.002668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate thermal effects on sudden changes and freezing of the quantum and classical correlations of remote qubits in a cavity quantum electrodynamics (CQED) network with losses. We find that the detrimental effect of thermal reservoirs on the freezing of correlations can be compensated via an efficient coupling of the fiber connecting the two cavities of the system. Furthermore, for certain initial conditions, we find a double sudden transition in the dynamics of Bures geometrical quantum discord. The second transition tends to disappear at a critical temperature, hence freezing the discord. Finally, we discuss the feasibility of the experimental realization of the present proposal.
Collapse
|
20
|
Chakraborty T, Singh H, Singh S, Gopal RK, Mitra C. Probing quantum discord in a Heisenberg dimer compound. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:425601. [PMID: 24067453 DOI: 10.1088/0953-8984/25/42/425601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrating the specific heat versus temperature data. Subsequently, quantum discord, total correlations and spin-spin correlation function are quantified from susceptibility and internal energy and plotted as a function of temperature. Violation of Bell's inequality is also tested for NH4CuPO4, H2O via both experimental susceptibility and specific heat data signifying the presence of entanglement.
Collapse
Affiliation(s)
- Tanmoy Chakraborty
- Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur Campus, PO: BCKV CampusMain Office, Mohanpur-741252, Nadia, West Bengal, India
| | | | | | | | | |
Collapse
|
21
|
Aguilar GH, Farías OJ, Maziero J, Serra RM, Ribeiro PHS, Walborn SP. Experimental estimate of a classicality witness via a single measurement. PHYSICAL REVIEW LETTERS 2012; 108:063601. [PMID: 22401071 DOI: 10.1103/physrevlett.108.063601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Indexed: 05/31/2023]
Abstract
The perception that quantum correlations can still appear in separable states has opened exciting new possibilities regarding their use as a resource in quantum information science. Quantifying such quantum correlations involves the complete knowledge of the system's state and numerical optimization procedures. Thus, it is natural to seek methods involving fewer measurements that indicate the nature of the correlations in a system. Here we propose a classicality witness that can be accurately estimated via statistics from a single measurement and perform an experiment to explore the utility of this witness for quantum states with different types of correlations.
Collapse
Affiliation(s)
- G H Aguilar
- Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil.
| | | | | | | | | | | |
Collapse
|
22
|
Streltsov A, Kampermann H, Bruss D. Behavior of quantum correlations under local noise. PHYSICAL REVIEW LETTERS 2011; 107:170502. [PMID: 22107493 DOI: 10.1103/physrevlett.107.170502] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2011] [Indexed: 05/31/2023]
Abstract
We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.
Collapse
Affiliation(s)
- Alexander Streltsov
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik III, D-40225 Düsseldorf, Germany.
| | | | | |
Collapse
|
23
|
Auccaise R, Céleri LC, Soares-Pinto DO, deAzevedo ER, Maziero J, Souza AM, Bonagamba TJ, Sarthour RS, Oliveira IS, Serra RM. Environment-induced sudden transition in quantum discord dynamics. PHYSICAL REVIEW LETTERS 2011; 107:140403. [PMID: 22107179 DOI: 10.1103/physrevlett.107.140403] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Indexed: 05/31/2023]
Abstract
Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.
Collapse
Affiliation(s)
- R Auccaise
- Empresa Brasileira de Pesquisa Agropecuária, Rua Jardim Botânico 1024, 22460-000 Rio de Janeiro, Rio de Janeiro, Brazil
| | | | | | | | | | | | | | | | | | | |
Collapse
|
24
|
Auccaise R, Maziero J, Céleri LC, Soares-Pinto DO, deAzevedo ER, Bonagamba TJ, Sarthour RS, Oliveira IS, Serra RM. Experimentally witnessing the quantumness of correlations. PHYSICAL REVIEW LETTERS 2011; 107:070501. [PMID: 21902378 DOI: 10.1103/physrevlett.107.070501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Indexed: 05/31/2023]
Abstract
The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.
Collapse
Affiliation(s)
- R Auccaise
- Empresa Brasileira de Pesquisa Agropecuária, Rio de Janeiro, Brazil
| | | | | | | | | | | | | | | | | |
Collapse
|