  Via the AdS/CFT correspondence, fundamental constraints on the entanglement
structure of quantum systems translate to constraints on spacetime geometries
that must be satisfied in any consistent theory of quantum gravity. In this
paper, we investigate such constraints arising from strong subadditivity and
from the positivity and monotonicity of relative entropy in examples with
highly-symmetric spacetimes. Our results may be interpreted as a set of energy
conditions restricting the possible form of the stress-energy tensor in
consistent theories of Einstein gravity coupled to matter.
