Seeing the entanglement wedge

Adam Levine,Arvin Shahbazi-Moghaddam,Ronak M Soni

doi:10.1007/jhep06(2021)134

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.

Highlights

For the encoding of WE[A] ∩ WC[A] to be possible
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

Summary

Introduction

For the encoding of WE[A] ∩ WC[A] to be possible. If we freeze gravity while holding M fixed, the bulk Hilbert space reduces to that of QFT on a curved background M and all bulk operators in WC[A] would exactly commute with CFT operators in D(A), rendering bulk reconstruction impossible in WE[A] ∩ WC[A]. A first step towards a Lorentzian bulk interpretation of entanglement wedge reconstruction would be to use such semi-classical operations to bring parts of WE[A] ∩ WC[A] into either the causal past or causal future of D(A) This would make explicit the non-commutativity of simple CFT operators in D(A) with bulk operators in WE[A] ∩ WC[A]. Coordinated action between these left and right observers, can send in a pulse of negative energy that moves the causal horizon so that the observers may access some of the interior While this may not seem to be a direct example of seeing the entanglement wedge since the black hole interior of the thermo-field double is already in the future of the boundary, in section 3 we discuss a simple variant of this set-up, first described in [27], where backreaction can bring previously space-like separated regions into causal contact with the boundary..

Objectives

Discussion

Conclusion