Characterizing quantum correlations in spin chains

Abstract

The growth in the demand for precisely crafted many-body systems of spin-$1/2$ particles/qubits is due to their top-notch versatility in application-oriented quantum-enhanced protocols and the fundamental tests of quantum theory. Here we address the question: how quantum is a chain of spins? We demonstrate that a single element of the density matrix carries the answer. Properly analyzed it brings information about the extent of the many-body entanglement and the non-locality. This method can be used to tailor and witness highly non-classical effects in many-body systems with possible applications to quantum computing, ultra-precise metrology or large-scale tests of quantum mechanics. As a proof of principle, we investigate the extend of non-locality and entanglement in ground states and thermal states of experimentally accessible spin chains.

arXiv comment9 pages, 6 figures

References in corpus (58)

• Quantum entanglement
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum Simulation
• Bell nonlocality
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum metrology with nonclassical states of atomic ensembles
• On the volume of the set of mixed entangled states
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Scalable multi-particle entanglement of trapped ions
• Measuring entanglement entropy through the interference of quantum many-body twins
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• An Area Law for One Dimensional Quantum Systems
• Nonlinear atom interferometer surpasses classical precision limit
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Atom chip based generation of entanglement for quantum metrology
• Quantum Inverse Scattering Method and Correlation Functions
• Squeezing and entanglement in a Bose-Einstein condensate
• Quantum entanglement in condensed matter systems
• Fisher information and multiparticle entanglement
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Tensor networks for complex quantum systems
• Multipartite entanglement and high precision metrology
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Fisher Information and entanglement of non-Gaussian spin states
• Measuring multipartite entanglement via dynamic susceptibilities
• An introduction to integrable techniques for one-dimensional quantum systems
• Bell Correlations in a Bose-Einstein Condensate
• Spin chains and combinatorics
• Detecting non-locality in multipartite quantum systems with two-body correlation functions
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Orientation-Dependent Entanglement Lifetime in a Squeezed Atomic Clock
• Two-Qubit State Tomography using a Joint Dispersive Read-Out
• Multi-Element Logic Gates for Trapped-Ion Qubits
• Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions
• Unified criteria for multipartite quantum nonlocality
• Entanglement entropy of two disjoint blocks in critical Ising models
• Renyi Entropy of the XY Spin Chain
• The entanglement negativity in random spin chains
• Bell inequalities for continuous-variable correlations
• Entanglement negativity in the critical Ising chain
• Ideal n-body correlations with massive particles
• Emptiness Formation Probability for the One-Dimensional Isotropic XY Model
• Entanglement, EPR steering, and Bell-nonlocality criteria for multipartite higher-spin systems
• Accurate mapping of multilevel Rydberg atoms on interacting spin-$1/2$ particles for the quantum simulation of Ising models
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• A strong Bell correlation witness between spatially separated pairs of atoms
• Bell inequalities for Continuous-Variable Measurements
• Emptiness Formation Probability for the Anisotropic XY Spin Chain in a Magnetic Field
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Floating Phase in 1D Transverse ANNNI Model
• Entanglement and classical fluctuations at finite-temperature critical points
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model
• Formation probabilities in quantum critical chains and Casimir effect

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