Thermal state entanglement in harmonic lattices

Abstract

We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites are shown to be entangled only due to boundary effects. Other forms of entanglement are addressed in the second part of the paper by using the energy as witness of entanglement. We close with a comprehensive diagram showing the different phases of entanglement versus complete separability and propose techniques to swap and tune entanglement experimentally.

9 pages, 4 figures

References in corpus (14)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Universal Quantum Computation with Continuous-Variable Cluster States
• Bound entangled Gaussian states
• Entanglement Properties of the Harmonic Chain
• Entanglement Witnesses in Spin Models
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
• Entanglement Observables and Witnesses for Interacting Quantum Spin Systems
• Thermal bound entanglement in macroscopic systems and area laws
• Detecting entanglement with a thermometer
• Spatial Entanglement From Off-Diagonal Long Range Order in a BEC

Cited by in corpus (63)

• Entanglement negativity in extended systems: A field theoretical approach
• Finite temperature entanglement negativity in conformal field theory
• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Entanglement negativity in the harmonic chain out of equilibrium
• Entanglement negativity after a global quantum quench
• On the partial transpose of fermionic Gaussian states
• Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Symmetry decomposition of negativity of massless free fermions
• Twisted and untwisted negativity spectrum of free fermions
• Entanglement negativity in two-dimensional free lattice models
• Topological entanglement negativity in Chern-Simons theories
• Finite-temperature entanglement negativity of free fermions
• Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions
• Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion
• System-bath entanglement in nanothermodynamics
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions
• Entanglement negativity and sudden death in the toric code at finite temperature
• Entanglement dynamics in presence of diversity under decohering environments
• Quantum field thermal machines
• Partial transpose of two disjoint blocks in XY spin chains
• Avoiding dissipation in a system of three quantum harmonic oscillators
• Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories
• Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance
• Negativity Spectrum in the Random Singlet Phase
• Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment
• Entangling two distant oscillators with a quantum reservoir
• Structure of Quantum Entanglement at a Finite Temperature Critical Point
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Entanglement negativity in free-fermion systems: An overlap matrix approach
• Bell-inequality test of spatial mode entanglement of a single massive particle
• Exact decoherence-free state of two distant quantum systems in a non-Markovian environment
• Gaussian entanglement induced by an extended thermal environment
• Quantum entanglement between the electron clouds of nucleic acids in DNA
• Dynamical and quantum effects of collective dissipation in optomechanical systems
• Gaussian tripartite entanglement out of equilibrium
• Quantum Entanglement at High Temperatures? II. Bosonic Systems in Nonequilibrium Steady State
• Entangling two defects via a surrounding crystal
• Numerical renormalization group method for entanglement negativity at finite temperature
• Quantum reservoirs with ion chains
• Statistical mechanics of entanglement mediated by a thermal reservoir I
• "Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny
• Entanglement at the quantum phase transition in a harmonic lattice
• Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators
• Enhanced entanglement in multi-bath spin-boson models
• Dynamical paths and universality in continuous variables open systems
• Perturbative expansion of entanglement negativity using patterned matrix calculus
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Quantum thermalization and thermal entanglement in the open quantum Rabi model
• Symmetry protected entanglement in random mixed states
• Pathways toward understanding Macroscopic Quantum Phenomena
• Single-shot energetic-based estimator for entanglement in a half-parity measurement setup
• Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving
• Long-time equilibration can determine transient thermality
• The Fate of Entanglement
• Finite-temperature quantum discordant criticality
• Fluctuation-Dissipation Relation for a Quantum Brownian Oscillator in a Parametrically Squeezed Thermal Field
• A contour for the entanglement negativity of bosonic Gaussian states
• Entanglement Generalization in Coupled Harmonic Oscillators
• Quantum Information Approaches to Quantum Gravity
• On the diagonalization of quadratic Hamiltonians