Generalized Entanglement Wedges and the Connected Wedge Theorem
Athira Arayath, Sabrina Pasterski
TLDR
This paper rephrases the Connected Wedge Theorem using generalized entanglement wedges, establishing new bounds on mutual information and extending the theorem.
Key contributions
- Rephrases the Connected Wedge Theorem (CWT) using generalized entanglement wedges.
- Establishes new upper and lower bounds on boundary mutual information via bulk region entropies.
- Defines new bulk decision regions where scattering implies a connected entanglement wedge.
- Extends the generalized CWT framework to asymptotically flat spacetimes.
Why it matters
This paper provides a new framework for understanding the Connected Wedge Theorem, linking it to bulk region entanglement entropies. It offers new bounds on mutual information and expands the theorem's applicability to asymptotically flat spacetimes. This advances our understanding of holographic entanglement.
Original 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.
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