Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

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.

Published version, 4 pages + appendices & references, 4 figures in the main text

References in corpus (13)

• Probing many-body dynamics on a 51-atom quantum simulator
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Single-Spin Addressing in an Atomic Mott Insulator
• Area laws in quantum systems: mutual information and correlations
• Quantum magnetism and criticality
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• A Quantum Gas Microscope for Fermionic Atoms
• Quantum gas microscopy for single atom and spin detection
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Eta-pairing states as true scars in an extended Hubbard Model
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• 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
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras