Generalized Entanglement Wedges and the Connected Wedge Theorem

TL;DR

This paper extends the connected wedge theorem using generalized entanglement wedges, establishing bounds on mutual information and connecting scattering configurations to entanglement wedge connectivity, even in flat spacetimes.

Contribution

It introduces a generalized framework for entanglement wedges, providing new bounds on mutual information and extending the connected wedge theorem to flat spacetimes.

Findings

Established new bounds on boundary mutual information in terms of bulk entropies.

Defined new bulk decision regions linking scattering configurations to entanglement wedge connectivity.

Extended the connected wedge theorem to asymptotically flat spacetimes.

Abstract

We use the framework of generalized entanglement wedges to revisit the connected wedge theorem (CWT). This construction identifies an entanglement wedge associated for any bulk region and allows us to rephrase the CWT in terms of the entanglement entropies of bulk regions. We establish new upper and lower bounds on the mutual information of boundary decision regions in terms of the entropies of certain bulk regions associated with a scattering configuration. We then define new bulk decision regions for which we show that a non-empty scattering configuration implies a connected entanglement wedge. This generalization of the CWT extends to asymptotically flat spacetimes.