Area laws in quantum systems: mutual information and correlations

Abstract

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entropy serves as a guiding principle in the search for the fundamental laws of Planck-scale physics. In this paper we show that a similar phenomenon emerges from the established laws of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of microscopic degrees of freedom, it may diverge as the inverse temperature in quantum systems. A rigorous relation between area laws and correlations is established and their explicit behavior is revealed for a large class of quantum many-body states beyond equilibrium systems.

5 pages, 2 figures, published version with appendix

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• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Multipoint entanglement in disordered systems
• Entangled quantum cellular automata, physical complexity, and Goldilocks rules
• Entanglement and private information in many-body thermal states
• Spread of Entanglement in Non-Relativistic Theories
• Entanglement transitions in a boundary-driven open quantum many-body system
• Entanglement of Vacuum States With the de Sitter Horizon: Consequences on Holographic Dark Energy
• Extended string-net models with all anyons at finite temperature
• A holographic realization of correlation and mutual information
• Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
• Scalable Heteronuclear Architecture of Neutral Atoms Based on EIT
• Geometrical picture of the electron-electron correlation at the large-D limit
• Correlation functions in expanding universes
• Order parameter conditions from mutual information and symmetry conditions
• Attention to Quantum Complexity
• Chaotic spin-spin entanglement on a recursive lattice
• Role of external fields in enhancing long-distance entanglement at finite temperatures
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Fast Scramblers, Democratic Walks and Information Fields
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Entanglement transition in unitary system-bath dynamics
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• On the Relative Distance of Entangled Systems in Emergent Spacetime Scenarios
• Quantum statistical gravity: time dilation due to local information in many-body quantum systems
• Gauging Quantum Phases: A Matrix Product State Approach
• Extracting filtered signal statistics of continuously measured quantum systems
• Transitions of the Lyapunov spectrum and entanglement entropy in monitored quantum dynamics with homogeneous unitary gates
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Entanglement signatures of a percolating quantum system
• Holographic entanglement renormalisation for fermionic quantum matter
• Tensor network states for the description of quantum many-body systems
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Multiscale complexity of two-dimensional Ising systems with short-range, ferromagnetic interactions
• Detecting entanglement with transport measurement in weakly interacting and fluctuating systems
• Quantum Circuits for Matrix-Product Unitaries
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• Continuous matrix product operators for quantum fields
• Geometric Rényi mutual information induced by localized particle excitations in quantum field theory
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems
• Bell sampling in Quantum Monte Carlo simulations
• Symmetry-protected topological wire in a topological vacuum
• Autangle: A case of Quantum Narcissism?
• Emergent geometry from entanglement structure
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Recent developments in the holographic description of quantum chaos
• Rényi entropy of single-character CFTs on the torus
• Mutual Information in Coupled Double Quantum Dots: A Simple Analytic Model for Potential Artificial Consciousness
• Quantum entanglement and the non-orientability of spacetime
• Symmetry-enforced minimal entanglement and correlation in quantum spin chains
• Order in Quantum Compass and Orbital $e_g$ Models
• A Information-Theoretic View on Spacetime
• Is monogamy of entanglement geometrical?
• Note on Mutual Information between Two Intervals of Extremal BTZ
• Mutual information in interacting spin systems
• Exact Mappings in Condensed Matter Physics
• Tachyonic quench in a free bosonic field theory
• Entanglement entropy of a simple quantum system