  The origin of black hole entropy and the black hole information problem
provide important clues for trying to piece together a quantum theory of
gravity. Thus far, discussions on this topic have mostly assumed that in a
consistent theory of gravity and quantum mechanics, quantum theory will be
unmodified. Here, we examine the black hole information problem in the context
of generalisations of quantum theory. In particular, we examine black holes in
the setting of generalised probabilistic theories, in which quantum theory and
classical probability theory are special cases. We compute the time it takes
information to escape a black hole, assuming that information is preserved. We
find that under some very general assumptions, the arguments of Page (that
information should escape the black hole after half the Hawking photons have
been emitted), and the black-hole mirror result of Hayden and Preskill (that
information can escape quickly) need to be modified. The modification is
determined entirely by what we call the Wootters-Hardy parameter associated
with a theory. We find that although the information leaves the black hole
after enough photons have been emitted, it is fairly generic that it fails to
appear outside the black hole at this point -- something impossible in quantum
theory due to the no-hiding theorem. The information is neither inside the
black hole, nor outside it, but is delocalised. Our central technical result is
an information decoupling theorem which holds in the generalised probabilistic
framework.
