Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
arXiv:2108.12209 · doi:10.1103/PhysRevX.12.021022
Abstract
Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.
arXiv comment43 pages, 5 figures, [v.2] small improvement [v.3, v.4] published version, [v5] Added Appendix I to correct Proposition 9 and preserve the main results
References in corpus (159)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- The density-matrix renormalization group in the age of matrix product states
- Separability of Mixed States: Necessary and Sufficient Conditions
- Introducing Quantum Discord
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Quantifying Coherence
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Quantifying Entanglement
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Quantum Coherence as a Resource
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Entanglement entropy and conformal field theory
- Entanglement in a simple quantum phase transition
- Entanglement Measures and Purification Procedures
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- The Role of Relative Entropy in Quantum Information Theory
- Entanglement renormalization
- Zoo of quantum-topological phases of matter
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Quantum metrology from a quantum information science perspective
- Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
- Quantum entanglement in condensed matter systems
- Quantum Fisher information matrix and multiparameter estimation
- Area laws in quantum systems: mutual information and correlations
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Fisher information and multiparticle entanglement
- Spectral Gap and Exponential Decay of Correlations
- Entanglement versus Correlations in Spin Systems
- "Squashed Entanglement" - An Additive Entanglement Measure
- A complete family of separability criteria
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Bound entanglement can be activated
- Measures and applications of quantum correlations
- Aspects of generic entanglement
- Measuring multipartite entanglement via dynamic susceptibilities
- The entanglement of purification
- Quantum conditional mutual information and approximate Markov chains
- Continuity of quantum conditional information
- Critical Quantum metrology with a finite-component quantum phase transition
- Quantifying Entanglement with Witness Operators
- Quantum Coherence via Skew Information and Its Polygamy
- Propagation of Correlations in Quantum Lattice Systems
- Macroscopic quantum states: measures, fragility and implementations
- Separability and entanglement of composite quantum systems
- Nearly-linear light cones in long-range interacting quantum systems
- Macroscopicity of Mechanical Quantum Superposition States
- Long-range quantum entanglement in noisy cluster states
- Faithful Squashed Entanglement
- Dynamic framework for criticality-enhanced quantum sensing
- Finite temperature entanglement negativity in conformal field theory
- Characterization of separable states and entanglement witnesses
- Entropy and Entanglement in Quantum Ground States
- Locality in Quantum and Markov Dynamics on Lattices and Networks
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Long-distance entanglement in spin systems
- Sensitivity Bounds for Multiparameter Quantum Metrology
- Hamiltonian complexity
- A short review on entanglement in quantum spin systems
- Exponential Decay of Correlations Implies Area Law
- Topological Order at Non-zero Temperature
- Bringing entanglement to the high temperature limit
- Extremal properties of the variance and the quantum Fisher information
- Irreversibility for all bound entangled states
- Entanglement negativity in the harmonic chain out of equilibrium
- Quantum critical metrology
- Quantum Hamiltonian Complexity
- Bounds on Information Propagation in Disordered Quantum Spin Chains
- An area law for entanglement from exponential decay of correlations
- High Temperature Macroscopic Entanglement
- Locality of temperature
- Sample-efficient learning of quantum many-body systems
- At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
- Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
- Measures of macroscopicity for quantum spin systems
- Fisher Information in Noisy Intermediate-Scale Quantum Applications
- Finite speed of quantum scrambling with long range interactions
- Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
- An area law for the entropy of low-energy states
- Strictly linear light cones in long-range interacting systems of arbitrary dimensions
- Quantum Belief Propagation
- The asymptotic relative entropy of entanglement
- Continuity bounds for entanglement
- Hierarchy of linear light cones with long-range interactions
- The Lieb-Robinson light cone for power-law interactions
- A short note on passivity, complete passivity and virtual temperatures
- Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
- Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
- Negative eigenvalues of partial transposition of arbitrary bipartite states
- Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox
- Continuity bounds on the quantum relative entropy
- Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
- Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
- Most energetic passive states
- Multipartite Entanglement at Finite Temperature
- Continuity bounds on the quantum relative entropy - II
- Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
- Information propagation for interacting particle systems
- Entanglement vs. gap for one-dimensional spin systems
- Detection of Macroscopic Entanglement by Correlation of Local Observables
- Experimental realisation of multipartite entanglement via quantum Fisher information in a uniform antiferromagnetic quantum spin chain
- Finite-temperature entanglement negativity of free fermions
- Connecting global and local energy distributions in quantum spin models on a lattice
- Absence of fast scrambling in thermodynamically stable long-range interacting systems
- Entanglement Renyi negativity across a finite temperature transition: a Monte Carlo study
- On asymptotic continuity of functions of quantum states
- Reconstructing the quantum critical fan of strongly correlated systems via quantum correlations
- Simulating Bosonic Baths with Error Bars
- Energetic instability of passive states in thermodynamics
- Supersonic quantum communication
- Skew informations from an operational view via resource theory of asymmetry
- Relative entropy and squashed entanglement
- Closed formula for the relative entropy of entanglement
- Coherence distillation machines are impossible in quantum thermodynamics
- General expressions for the quantum Fisher information matrix with applications to discrete quantum imaging
- Quantum Approximate Markov Chains are Thermal
- Decay of Correlations in Fermi Systems at Non-zero Temperature
- Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
- Some Properties of Correlations of Quantum Lattice Systems in Thermal Equilibrium
- Lieb-Robinson bounds for spin-boson lattice models and trapped ions
- Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
- Information-theoretical analysis of topological entanglement entropy and multipartite correlations
- Global passivity in microscopic thermodynamics
- Stability of topologically invariant order parameters at finite temperature
- Perturbative analysis of topological entanglement entropy from conditional independence
- Exponential decay of mutual information for Gibbs states of local Hamiltonians
- Structure of Quantum Entanglement at a Finite Temperature Critical Point
- Quantum Fisher Information as the Convex Roof of Variance
- Modular Entanglement
- Finite speed of quantum information in models of interacting bosons at finite density
- Eigenstate thermalization from the clustering property of correlation
- Nonadditivity of Rains' bound for distillable entanglement
- Long-range entanglement is necessary for a topological storage of quantum information
- Extensions of Lieb's concavity theorem
- Entanglement transitions as a probe of quasiparticles and quantum thermalization
- On convex optimization problems in quantum information theory
- Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature
- Quantum correlations, separability and quantum coherence length in equilibrium many-body systems
- Thermal States as Convex Combinations of Matrix Product States
- Quantum macroscopicity versus distillation of macroscopic superpositions
- Quantum macroscopicity measure for arbitrary spin systems and its application to quantum phase transitions
- Local integrals of motion and the logarithmic lightcone in many-body localized systems
- On the negativity of random pure states
- Quantum Markov Networks and Commuting Hamiltonians
- Scaling of macroscopic superpositions close to a quantum phase transition
- General conditions for the generation of long-distance entanglement
- Uncertainty relation based on Wigner-Yanase-Dyson skew information with quantum memory
- Maximization of thermal entanglement of arbitrarily interacting two qubits
- Total correlations as fully additive entanglement monotones
- Circuit lower bounds for low-energy states of quantum code Hamiltonians
- Investigation of commuting Hamiltonian in quantum Markov network
Cited by in corpus (15)
- Speed limits and locality in many-body quantum dynamics
- Strong quantum metrological limit from many-body physics
- Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
- Localized Virtual Purification
- Thermal Area Law in Long-Range Interacting Systems
- Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
- Reconstructing the spatial structure of quantum correlations in materials
- Clustering theorem in 1D long-range interacting systems at arbitrary temperatures
- Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
- Symmetry: a fundamental resource for quantum coherence and metrology
- Measuring multipartite quantum correlations by thermodynamic work extraction
- Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
- Locality bounds for quantum dynamics at low energy
- Stability of thermal equilibrium in long-range quantum systems
- Entanglement and private information in many-body thermal states