Nonlocality in many-body quantum systems detected with two-body correlators

Abstract

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

46 pages (25.2 + appendices), 7 figures

References in corpus (25)

• Device-independent security of quantum cryptography against collective attacks
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Criticality, the area law, and the computational power of PEPS
• Quantum many-body models with cold atoms coupled to photonic crystals
• Entanglement versus Correlations in Spin Systems
• Atom-Light Interactions in Photonic Crystals
• Fisher Information and entanglement of non-Gaussian spin states
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Subwavelength vacuum lattices and atom-atom interactions in photonic crystals
• Private Randomness Expansion With Untrusted Devices
• Experimental entanglement of a six-photon symmetric Dicke state
• Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
• Detecting multiparticle entanglement of Dicke states
• Quantum Non-Demolition Detection of Strongly Correlated Systems
• Permutationally invariant state reconstruction
• Multipartite entanglement detection via structure factors
• Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation
• Entanglement and nonlocality are inequivalent for any number of particles
• Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations
• Shot-noise-limited magnetometer with sub-pT sensitivity at room temperature
• Translationally invariant multipartite Bell inequalities involving only two-body correlators
• Hybrid Quantum System of a Nanofiber Mode Coupled to Two Chains of Optically Trapped Atoms
• Detecting genuine multipartite entanglement of pure states with bipartite correlations

Cited by in corpus (41)

• Entanglement between two spatially separated atomic modes
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Randomness in Quantum Mechanics: Philosophy, Physics and Technology
• Scalable Bell inequalities for qubit graph states and robust self-testing
• Machine Learning Bell Nonlocality in Quantum Many-body Systems
• Device-independent witnesses of entanglement depth from two-body correlators
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Bell correlations depth in many-body systems
• Energy as a detector of nonlocality of many-body spin systems
• Bounding the set of classical correlations of a many-body system
• Optimization of device-independent witnesses of entanglement depth from two-body correlators
• Bell inequalities violated using detectors of low efficiency
• Bell correlations at Ising quantum critical points
• Entanglement and Nonlocality in Infinite 1D Systems
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Entanglement and Nonlocality in Diagonal Symmetric States of $N$-qubits
• Bell correlations at finite temperature
• Collective randomized measurements in quantum information processing
• Testing Scalable Bell Inequalities for Quantum Graph States on IBM Quantum Devices
• Detecting Bell correlations in multipartite non-Gaussian spin states
• Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles
• Einstein-Podolsky-Rosen steering, depth of steering and planar spin squeezing in two-mode Bose-Einstein condensates
• Bounding the persistency of the nonlocality of W states
• Certificates of quantum many-body properties assisted by machine learning
• Symmetric quantum states: a review of recent progress
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Robustness of non-locality in many-body open quantum systems
• Nonlinear Bell inequality for macroscopic measurements
• Inherent quantum resources in stationary spin chains
• Characterizing nonlocality of pure symmetric three-qubit states
• Deriving three-outcome permutationally invariant Bell inequalities
• The sounds of science a symphony for many instruments and voices part II
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Experimental demonstration of the Bell-type inequalities for four qubit Dicke state using IBM Quantum Processing Units
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations
• Effects of Topological Boundary Conditions on Bell Nonlocality
• Nonlocality, Integrability and Quantum Chaos in the Spectrum of Bell Operators