Maximal Entangling Rates from Holography

TL;DR

This paper establishes new speed limits on entanglement growth and correlator evolution in holographic CFTs, revealing fundamental bounds and a momentum-entanglement correspondence with implications for quantum energy conditions.

Contribution

It introduces novel bounds on entanglement and correlator growth in holographic CFTs, proving a conjecture in 2d CFT and developing new geometric techniques in gravity.

Findings

Proves bounds on entanglement growth rates.

Validates a conjecture for 2d CFT states.

Establishes a momentum-entanglement correspondence.

Abstract

We prove novel speed limits on the growth of entanglement, equal-time correlators, and spacelike Wilson loops in spatially uniform time-evolving states in strongly coupled CFTs with holographic duals. These bounds can also be viewed as quantum weak energy conditions. Several of the speed limits are valid for regions of arbitrary size and with multiple connected components, and our findings imply new bounds on the effective entanglement velocity of small subregions. In 2d CFT, our results prove a conjecture by Liu and Suh for a large class of states. We also bound spatial derivatives of entanglement and correlators. Key to our findings is a momentum-entanglement correspondence, showing that entanglement growth is computed by the momentum crossing the HRT surface. In our setup, we prove a number of general features of boundary-anchored extremal surfaces, such as a sharp bound on the smallest radius that a surface can probe, and that the tips of extremal surfaces cannot lie in trapped regions. Our methods rely on novel global GR techniques, including a delicate interplay between Lorentzian and Riemannian Hawking masses. While our proofs assume the dominant energy condition in the bulk, we provide numerical evidence that our bounds are true under less restrictive assumptions.