201 research outputs found
Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions
We compute the asymptotic entanglement capacity of the Ising interaction ZZ,
the anisotropic Heisenberg interaction XX + YY, and more generally, any
two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an
entanglement assisted classical communication protocol using the Hamiltonian K
with rate equal to the asymptotic entanglement capacity.Comment: 5 pages, 1 figure; minor corrections, conjecture adde
Genuine quantum correlations in quantum many-body systems: a review of recent progress
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.Comment: Review. Close to published version. Comments are welcome! Please
write an email to g.dechiara[(at)]qub.ac.u
Coherent and dissipative dynamics at quantum phase transitions
The many-body physics at quantum phase transitions shows a subtle interplay
between quantum and thermal fluctuations, emerging in the low-temperature
limit. In this review, we first give a pedagogical introduction to the
equilibrium behavior of systems in that context, whose scaling framework is
essentially developed by exploiting the quantum-to-classical mapping and the
renormalization-group theory of critical phenomena at continuous phase
transitions. Then we specialize to protocols entailing the out-of-equilibrium
quantum dynamics, such as instantaneous quenches and slow passages across
quantum transitions. These are mostly discussed within dynamic scaling
frameworks, obtained by appropriately extending the equilibrium scaling laws.
We review phenomena at first-order quantum transitions as well, whose peculiar
scaling behaviors are characterized by an extreme sensitivity to the boundary
conditions, giving rise to exponentials or power laws for the same bulk system.
In the last part, we cover aspects related to the effects of dissipative
interactions with an environment, through suitable generalizations of the
dynamic scaling at quantum transitions. The presentation is limited to issues
related to, and controlled by, the quantum transition developed by closed
many-body systems, treating the dissipation as a perturbation of the critical
regimes, as for the temperature at the zero-temperature quantum transition. We
focus on the physical conditions giving rise to a nontrivial interplay between
critical modes and various dissipative mechanisms, generally realized when the
involved mechanism excites only the low-energy modes of the quantum
transitions.Comment: Review paper, 138 pages. Final version to appear in Physics Report
Reversible simulation of bipartite product Hamiltonians
Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.Comment: 10 page
Entanglement in Many-Body Systems
The recent interest in aspects common to quantum information and condensed
matter has prompted a prosperous activity at the border of these disciplines
that were far distant until few years ago. Numerous interesting questions have
been addressed so far. Here we review an important part of this field, the
properties of the entanglement in many-body systems. We discuss the zero and
finite temperature properties of entanglement in interacting spin, fermionic
and bosonic model systems. Both bipartite and multipartite entanglement will be
considered. At equilibrium we emphasize on how entanglement is connected to the
phase diagram of the underlying model. The behavior of entanglement can be
related, via certain witnesses, to thermodynamic quantities thus offering
interesting possibilities for an experimental test. Out of equilibrium we
discuss how to generate and manipulate entangled states by means of many-body
Hamiltonians.Comment: 61 pages, 29 figure
Entanglemend and topological soliton structures in Heisenberg spin models
Thesis (Doctoral)--Izmir Institute of Technology, Mathematics, Izmir, 2010Includes bibliographical references (leaves: 143-150)Text in English; Abstract: Turkish and Englishxi, 163 leavesQuantum entanglement and topological soliton characteristics of spin models are studied. By identifying spin states with qubits as a unit of quantum information, quantum information characteristic as entanglement is considered in terms of concurrence. Eigenvalues, eigenstates, density matrix and concurrence of two qubit Hamiltonian of XY Z, pure DM, Ising, XY , XX, XXX and XXZ models with Dzialoshinskii- Moriya DM interaction are constructed. For time evolution of two qubit states, periodic and quasiperiodic evolution of entanglement are found. Entangled two qubit states with exchange interaction depending on distance J(R) between spins and influence of this distance on entanglement of the system are considered. Different exchange interactions in the form of Calogero- Moser type I, II, III and Herring-Flicker potential which applicable to interaction of Hydrogen molecule are used. For geometric quantum computations, the geometric (Berry) phase in a two qubit XX model under the DM interaction in an applied magnetic field is calculated. Classical topological spin model in continuum media under holomorphic reduction is studied and static N soliton and soliton lattice configurations are constructed. The holomorphic time dependent Schrödinger equation for description of evolution in Ishimori model is derived. The influence of harmonic potential and bound state of solitons are studied. Relation of integrable soliton dynamics with multi particle problem of Calogero-Moser type is established and N soliton and N soliton lattice motion are found. Special reduction of Abelian Chern-Simons theory to complex Burgers. hierarchy, the Galilean group, dynamical symmetry and Negative Burgers. hierarchy are found
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