  The Ryu-Takayanagi formula relates the entanglement entropy in a conformal
field theory to the area of a minimal surface in its holographic dual. We show
that this relation can be inverted for any state in the conformal field theory
to compute the bulk stress-energy tensor near the boundary of the bulk
spacetime, reconstructing the local data in the bulk from the entanglement on
the boundary. We also show that positivity, monotonicity, and convexity of the
relative entropy for small spherical domains between the reduced density
matrices of any state and of the ground state of the conformal field theory,
follow from positivity conditions on the bulk matter energy density. We discuss
an information theoretical interpretation of the convexity in terms of the
Fisher metric.
