Speed Limits for Entanglement

Abstract

We show that in any relativistic system, entanglement entropy obeys a speed limit set by the entanglement in thermal equilibrium. The bound is derived from inequalities on relative entropy with respect to a thermal reference state. Thus the thermal state constrains far-from-equilibrium entanglement dynamics whether or not the system actually equilibrates, in a manner reminiscent of fluctuation theorems in classical statistical mechanics. A similar shape-dependent bound constrains the full nonlinear time evolution, supporting a simple physical picture for entanglement propagation that has previously been motivated by holographic calculations in conformal field theory. We discuss general quantum field theories in any spacetime dimension, but also derive some results of independent interest for thermal relative entropy in 1+1d CFT.

16 pages

References in corpus (7)

• Towards a derivation of holographic entanglement entropy
• Thermalization of Strongly Coupled Field Theories
• Relative entropy and the Bekenstein bound
• Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
• Upper bounds on entangling rates of bipartite Hamiltonians
• Certain General Constraints on the Many-Body Localization Transition
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Cited by in corpus (16)

• On entanglement spreading in chaotic systems
• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• The entanglement spectrum of chiral fermions on the torus
• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Time evolution of entanglement for holographic steady state formation
• Spread of entanglement for small subsystems in holographic CFTs
• Chaos and entanglement spreading in a non-commutative gauge theory
• The Speed of Quantum Information Spreading in Chaotic Systems
• Modular Hamiltonian of a chiral fermion on the torus
• Equivalence of Emergent de Sitter Spaces from Conformal Field Theory
• Holographic Dual to Conical Defects: II. Colliding Ultrarelativistic Particles
• A First Law of Entanglement Rates from Holography
• Holographic thermalization in AdS-Gauss-Bonnet gravity for small entangled regions
• Holographic entanglement entropy for small subregions and thermalization of Born-Infeld AdS black holes
• Maximally entangling states and dynamics in one dimensional nearest neighbor Floquet systems
• Recent developments in the holographic description of quantum chaos