Entanglement and Nonlocality in Infinite 1D Systems

Abstract

We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.

Added a few references to related work. Closer to the published version

References in corpus (6)

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Cited by in corpus (23)

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• Single-copy entanglement detection
• Bounding the set of classical correlations of a many-body system
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• Bell correlations at Ising quantum critical points
• Inferring Nonlinear Many-Body Bell Inequalities From Average Two-Body Correlations: Systematic Approach for Arbitrary Spin-j Ensembles
• Entanglement marginal problems
• Bell correlations at finite temperature
• Detecting many-body Bell non-locality by solving Ising models
• Proving genuine multiparticle entanglement from separable nearest-neighbor marginals
• Resource Marginal Problems
• Introduction to quantum entanglement in many-body systems
• Two Dimensional Translation-Invariant Probability Distributions: Approximations, Characterizations and No-Go Theorems
• Deriving three-outcome permutationally invariant Bell inequalities
• Semi-device-independent information processing with spatiotemporal degrees of freedom
• Persistent nonlocality in an ultracold-atom environment
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations
• Entanglement detection with scrambled data
• Effects of Topological Boundary Conditions on Bell Nonlocality
• Trading symmetry for Hilbert-space dimension in Bell-inequality violation