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Speed Limits for Entanglement
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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.
Forward citations
Cited by 2 Pith papers
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The Speed of Quantum Information Spreading in Chaotic Systems
For chaotic systems with initial entanglement fraction f, quantum information spreads at speed v_E(f)/(1-f), interpolating between the entanglement speed at f=0 and the butterfly speed at f=1.
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The Quantum Null Energy Condition and Entanglement Entropy in Quenches
The QNEC gives a universal upper bound on the quadratic growth rate of quench entanglement entropy, and this bound is saturated by boundary state quenches.
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