Inviolable energy conditions from entanglement inequalities
  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. 
Nima Lashkari, Charles Rabideau, Philippe Sabella-Garnier, Mark Van   Raamsdonk
hep-th gr-qc