Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices
arXiv:2201.07236 · doi:10.1103/PhysRevResearch.4.L042037
Abstract
Correlation functions and entanglement are two different aspects to characterize quantum many-body states. While many correlation functions are experimentally accessible, entanglement entropy (EE), the simplest characterization of quantum entanglement, is usually difficult to measure. In this Letter, we propose a protocol to bound EE by local measurements. This protocol utilizes local correlation matrices and focuses on their (approximate) zero eigenvalues. Given a quantum state, each (approximate) zero eigenvalue can be used to define a set of local projection operators. An auxiliary Hamiltonian can then be constructed by summing these projectors. When the construction only involves projectors of zero eigenvalues, we prove the EE of a subsystem is bounded by the ground-state degeneracy of the auxiliary Hamiltonian on this subsystem. When projectors from nonzero eigenvalues are included, we show the EE can be bounded by a thermal entropy of the subsystem. Our protocol can be applied experimentally to investigate exotic quantum many-body states prepared in quantum simulators.
arXiv commentPublished version, 4 pages + appendices & references, 4 figures in the main text
References in corpus (56)
- Quantum Computing in the NISQ era and beyond
- Anyons in an exactly solved model and beyond
- Entanglement Entropy and Quantum Field Theory
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Probing many-body dynamics on a 51-atom quantum simulator
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Many-body localization, thermalization, and entanglement
- Geometric and Renormalized Entropy in Conformal Field Theory
- Entanglement entropy and conformal field theory
- A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
- Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
- Measuring entanglement entropy through the interference of quantum many-body twins
- Quantum thermalization through entanglement in an isolated many-body system
- Quantum many-body scars
- A Theory of Fault-Tolerant Quantum Computation
- Holographic Entanglement Entropy: An Overview
- Quantum entanglement in condensed matter systems
- Stabilizer Codes and Quantum Error Correction
- Single-Spin Addressing in an Atomic Mott Insulator
- Area laws in quantum systems: mutual information and correlations
- Probing entanglement entropy via randomized measurements
- Measuring the scrambling of quantum information
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Quantum magnetism and criticality
- Universal Quantum Estimator
- Direct estimations of linear and non-linear functionals of a quantum state
- Measuring entanglement growth in quench dynamics of bosons in an optical lattice
- A Quantum Gas Microscope for Fermionic Atoms
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
- Out-of-Time-Order Correlation for Many-Body Localization
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Does a single eigenstate encode the full Hamiltonian?
- Randomized benchmarking of single qubit gates in a 2D array of neutral atom qubits
- Efficient tomography of a quantum many-body system
- Out-of-time-ordered correlators in many-body localized systems
- Quantum gas microscopy for single atom and spin detection
- Unified structure for exact towers of scar states in the AKLT and other models
- Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
- Out-of-time-order correlations in many-body localized and thermal phases
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- Universal gates based on targeted phase shifts in a 3D neutral atom array
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- Determining a local Hamiltonian from a single eigenstate
- Eta-pairing states as true scars in an extended Hubbard Model
- Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
- Entanglement Hamiltonian Tomography in Quantum Simulation
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Coherent addressing of individual neutral atoms in a 3D optical lattice
- Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
- Multipartite entanglement detection in bosons
- Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension
- Efficient and feasible state tomography of quantum many-body systems
- Universal Logarithmic Scrambling in Many Body Localization
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- Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies
- Preparing Quantum States by Measurement-feedback Control with Bayesian Optimization
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