  Notoriously, quantum computation shatters complexity theory, but is innocuous
to computability theory. Yet several works have shown how quantum theory as it
stands could breach the physical Church-Turing thesis. We draw a clear line as
to when this is the case, in a way that is inspired by Gandy. Gandy formulates
postulates about physics, such as homogeneity of space and time, bounded
density and velocity of information --- and proves that the physical
Church-Turing thesis is a consequence of these postulates. We provide a quantum
version of the theorem. Thus this approach exhibits a formal non-trivial
interplay between theoretical physics symmetries and computability assumptions.
