  Magic can be distributed non-locally in many-body entangled states, such as
the low energy states of condensed matter systems. Using the Bravyi-Kitaev
magic state distillation protocol, we find that non-local magic is distillable
and can improve the distillation outcome. We analyze a few explicit examples
and show that spin squeezing can be used to convert non-distillable states into
distillable ones.
  Our analysis also suggests that the conventional product input states assumed
by magic distillation protocols are extremely atypical among general states
with distillable magic. It further justifies the need for studying a diverse
range of entangled inputs that yield magic states with high probability.
