Seeing the Entanglement Wedge

TL;DR

This paper proposes a unitary operation that allows a semiclassical observer to make the entanglement wedge causally accessible via backreaction, extending previous work to more complex boundary regions.

Contribution

It introduces a generalized unitary operation related to Connes Cocycle flow that reveals the entanglement wedge for unions of disjoint spherical caps.

Findings

The protocol works to first order in the size of the peninsula.

The construction generalizes previous work to disconnected spherical regions.

It relates to non-local couplings in quantum field theory.

Abstract

We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction. In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible `peninsula' into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the Appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.