  We study the interplay between magic and entanglement in quantum many-body
systems. We show that non-local magic, which is supported by the quantum
correlations is lower bounded by the non-flatness of entanglement spectrum and
upper bounded by the amount of entanglement in the system. We then argue that a
smoothed version of non-local magic bounds the hardness of classical
simulations for incompressible states. In conformal field theories, we
conjecture that the non-local magic should scale linearly with entanglement
entropy but sublinearly when an approximation of the state is allowed. We
support the conjectures using both analytical arguments based on unitary
distillation and numerical data from an Ising CFT. If the CFT has a holographic
dual, then we prove that the non-local magic vanishes if and only if there is
no gravitational back-reaction. Furthermore, we show that non-local magic is
approximately equal to the rate of change of the minimal surface area in
response to the change of cosmic brane tension in the bulk.
