Holographic pseudoentanglement and the complexity of the AdS/CFT dictionary

Understand

The `quantum gravity in the lab' paradigm suggests that quantum computers might shed light on quantum gravity by simulating the CFT side of the AdS/CFT correspondence and mapping the results to the AdS side.

• This relies on the assumption that the duality map (the `dictionary') is efficient to compute.
• In this work, we show that the complexity of the AdS/CFT dictionary is surprisingly subtle: there might be cases in which one can efficiently apply operators to the CFT state (a task we call 'operator reconstruction') without being able to extract basic properties of the dual bulk state such as its geometry (which we call 'geometry reconstruction').
• Geometry reconstruction corresponds to the setting where we want to extract properties of a completely unknown bulk dual from a simulated CFT boundary state.