Distillable entanglement and area laws in spin and harmonic-oscillator systems
arXiv:0705.3762 · doi:10.1103/PhysRevA.78.012335
Abstract
We address the presence of non-distillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions and topologies are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.
10 pages, 8 figures; v3: further results about spin systems added
References in corpus (30)
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement in quantum critical phenomena
- Scaling of Entanglement close to a Quantum Phase Transitions
- Entropy and Area
- Entanglement in a simple quantum phase transition
- Separability criterion and inseparable mixed states with positive partial transposition
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
- Area laws in quantum systems: mutual information and correlations
- Bound entangled Gaussian states
- Thermodynamics and the Measure of Entanglement
- Entanglement Properties of the Harmonic Chain
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Evidence for Bound Entangled States with Negative Partial Transpose
- Optimal spin squeezing inequalities detect bound entanglement in spin models
- An entanglement-area law for general bosonic harmonic lattice systems
- Distillability and partial transposition in bipartite systems
- A four-party unlockable bound-entangled state
- Optimal entanglement witnesses for continuous-variable systems
- Spatial structures and localization of vacuum entanglement in the linear harmonic chain
- Thermal bound entanglement in macroscopic systems and area laws
- Multipartite entanglement in quantum spin chains
- Quantum states on Harmonic lattices
- Bound entanglement in the XY model
- Two qubits can be entangled in two distinct temperature regions
- Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions
Cited by in corpus (31)
- Area laws for the entanglement entropy - a review
- Open-System Dynamics of Entanglement
- 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
- 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
- Topological entanglement negativity in Chern-Simons theories
- Finite-temperature entanglement negativity of free fermions
- Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion
- Spin structures and entanglement of two disjoint intervals in conformal field theories
- Entanglement negativity spectrum of random mixed states: A diagrammatic approach
- Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions
- Sudden death of distillability in qutrit-qutrit systems
- Distillability sudden death in qutrit-qutrit systems under global decoherence
- Distillability sudden death in qutrit-qutrit systems under amplitude damping
- The Negativity Hamiltonian: An operator characterization of mixed-state entanglement
- Negativity Spectrum in the Random Singlet Phase
- 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
- Macroscopic bound entanglement in thermal graph states
- Entanglement and magnetic order
- Work and Heat Value of Bound Entanglement
- Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
- Quench dynamics of Rényi negativities and the quasiparticle picture
- Symmetry protected entanglement in random mixed states
- Quench dynamics of negativity Hamiltonians