Statement
Problem 2.2 of Goto et al.: a quantum computer in a bulk subregion performs a task; by holographic duality the same task must be implementable on the boundary. What does bulk causal structure imply for boundary tasks, and conversely? The paper points to the connected wedge theorem relating bulk causal contact to preshared correlations and nonlocality on the boundary.
Why It Matters
Peripheral to the group’s current lines, but adjacent to the holographic-bell-program: the connected-wedge theorem is a statement about nonlocality/entanglement required for a boundary task, which is the same currency as Bell-CHSH. A long-run bridge, not a near-term calculation.
What We Know
- The connected wedge theorem (May et al.) ties bulk causal features to boundary entanglement needed to complete a task with prescribed inputs/outputs.
- Bulk causality is encoded in boundary micro-causality plus the holographic dictionary.
Possible Approaches
- Read connected-wedge-type constraints as Bell/nonlocality statements on boundary subalgebras.
- Relate to -routing / non-local quantum computation, which already surfaced in the embezzlement-capacity-project.