The study of black holes have revealed a deep connection between quantum information and spacetime geometry. Its origin must lie in the quantum theory of gravity we seek. Precise formulations of this relation have already led to new insights in Quantum Field Theory, some of which we have been rigorously proven. An important example is out discovery of the first universal lower bound on the local energy density. The energy near a point can be negative but it is bounded below by a quantity related to the information flowing past the point.