  In most approaches to fundamental physics, spacetime symmetries are
postulated a priori and then explicitly implemented in the theory. This
includes Lorentz covariance in quantum field theory and diffeomorphism
invariance in quantum gravity, which are seen as fundamental principles to
which the final theory has to be adjusted. In this paper, we suggest, within a
much simpler setting, that this kind of reasoning can actually be reversed, by
taking an operational approach inspired by quantum information theory. We
consider observers in distinct laboratories, with local physics described by
the laws of abstract quantum theory, and without presupposing a particular
spacetime structure. We ask what information-theoretic effort the observers
have to spend to synchronize their descriptions of local physics. If there are
"enough" observables that can be measured universally on several different
quantum systems, we show that the observers' descriptions are related by an
element of the orthochronous Lorentz group O^+(3,1), together with a global
scaling factor. Not only does this operational approach predict the Lorentz
transformations, but it also accurately describes the behavior of relativistic
Stern-Gerlach devices in the WKB approximation, and it correctly predicts that
quantum systems carry Lorentz group representations of different spin. This
result thus hints at a novel information-theoretic perspective on spacetime.
