Emergence of spacetime from quantum entanglement

4 problems

• Entanglement-geometry relation outside anti-de Sitter space

  Open

  The rule that entanglement equals area of a surface in the bulk is established for spaces with negative vacuum energy. Whether a version holds in flat or expanding spacetimes is unknown.

• Holographic entropy inequalities for six regions

  Partially resolved

  Entanglement between regions of a holographic system obeys special inequalities that general quantum systems need not obey. The full list is known only up to five regions.

• Which conformal field theories have a semiclassical gravity dual

  Partially resolved

  Only special quantum theories behave as if they described a smooth curved space with ordinary gravity. The exact conditions that single them out are unknown.

• Derive full nonlinear Einstein equations from boundary entanglement

  Partially resolved

  Small ripples of spacetime obeying Einstein's equations have been derived from rules about entanglement. The same for strongly curved spacetime has not been done.