Abstract:

Holography proposes that gravity in a region of space can be described by a quantum theory on its boundary. This raises the prospect of studying gravity by simulating the boundary theory on a quantum computer, provided the relevant parts of the bulk–boundary dictionary can be computed efficiently. One part of this dictionary relates readily measurable features of bulk geometry to quantum entanglement in the boundary theory. Yet quantum pseudoentanglement allows ensembles of states to have different entanglement structures while remaining computationally indistinguishable. This suggests that the dictionary may not be efficiently computable. Pseudoentanglement alone, however, does not establish that the holographic dictionary is hard to compute. Holographic boundary states are not generic quantum states, and their additional structure may allow entanglement to be measured efficiently. In this talk, I will present constructions of pseudoentanglement that exhibit properties relevant to holographic boundary states. The constructions use graphs to describe networks of entangled subsystems. I will explain how connectivity and edge-disjoint spanning trees allow independent operations on the subsystems to conceal their entanglement structure. I will also describe how these constructions allow a finer property of quantum correlations relevant to holography, called nonlocal magic, to be varied while keeping entanglement differences computationally hidden.

No prior knowledge of holography or pseudoentanglement will be assumed.