Holographic scattering requires a connected entanglement wedge (1912.05649v3)

Abstract: In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in connection with boundary correlation functions. We show that boundary regions associated with these scattering configurations must have $O(1/G_N)$ mutual information, and hence a connected entanglement wedge. One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory. We improve that argument to make it robust to small errors and provide a proof in the bulk using focusing arguments in general relativity. We also provide a direct link to entanglement wedge reconstruction by showing that the bulk scattering region must lie inside the connected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.

• The paper demonstrates that specific 2-to-2 bulk scattering processes in (2+1)-dimensional AdS yield connected entanglement wedges with O(1/GN) mutual information.
• The paper employs operational quantum tasks and classical null surface constructions to validate the link between bulk scattering and boundary entanglement.
• The paper’s findings imply that enhanced mutual information in boundary regions enables efficient nonlocal quantum operations, refining our understanding of holographic duality.

Entanglement Wedge and Bulk Scattering in AdS/CFT

This paper explores an intriguing aspect of the AdS/CFT correspondence, particularly focusing on the relationship between bulk scattering and boundary entanglement. In AdS/CFT duality, events or configurations that are seemingly impossible on the boundary but can occur within the bulk provide crucial insights into holography. This research assesses such configurations, identifying new implications for entanglement wedges associated with boundary regions in bulk scattering scenarios. The paper argues that for certain boundary conditions, the bulk scattering region is inherently connected with the entanglement wedge, and provides proof based on both operational quantum information theory and classical general relativity.

The paper introduces the concept of $2$-to-$2$ bulk scattering processes in $(2+1)$-dimensional asymptotically Anti-de Sitter spaces, where boundary configurations are impractical yet feasible in the bulk. Such configurations have historically been linked with singularities in holographic correlation functions but are now linked to significant mutual information and a connected entanglement wedge.

Key Findings

1. Connected Entanglement Wedge: The research shows that whenever specific boundary regions are linked to scattering processes, they exhibit $O(1/G_N)$ mutual information, indicating a connected entanglement wedge. This connectivity is vital for demonstrating that bulk scattering regions correspond to entangled boundary regions.
2. Operational Quantum Proof: Using quantum computational tasks, the authors argue that high mutual information is required for successful completion of certain tasks correlated with scattering configurations. This requirement implies that boundary regions must have significant mutual information when mediated by entangled states.
3. General Relativity Verification: Classical general relativity is employed to verify the findings from quantum theory. By illustrating the construction of null surfaces and their intersections, the research demonstrates how the entanglement wedge must be connected to accommodate the differences in areas of intersecting surfaces.
4. Causal Structure: The work enforces the understanding that entanglement wedge structures are intricately linked to the causal structure of the bulk. The boundary regions' causal limits, as delineated by lightsheets and extremal surfaces in the bulk, structurally influence the entanglement wedge.

Implications

This paper not only confirms existing beliefs about holography but also presents a broader perspective on how nonlocal computations may require less information than previously thought when conducted in the holographic paradigm. The authors suggest that the AdS/CFT correspondence inherently ensures efficient nonlocal operations that are exponentially more resource-effective than classical operations. This finding is potent, indicating potential advancements in understanding quantum cryptographic protocols and providing evidence for exponentially efficient quantum computation strategies.

The work has implications for theoretical constructs like the ER=EPR conjecture and the understanding of spacetime geometry encoded within quantum information. It shines light on how entanglement geometrically influences the nature of dual spacetimes under the AdS/CFT framework, reinforcing the notion that spacetime, in such contexts, is indeed a construct arising from entanglement.

Conclusion and Future Directions

The paper concludes without asserting the novelty of this research as groundbreaking but underscores its contribution to the synergy between quantum information theory and spacetime geometry. It lays a foundation for future inquiries into higher-dimensional configurations and alternatives to prove connectedness in entanglement wedges directly from quantum information perspectives or correlation function analysis. Additionally, this research poses exciting prospects for developing methodologies to decode quantum spacetime from entangled boundary configurations.