  Bell's seminal paper shows that some correlations in quantum theory are not
reconcilable with hidden variables and the classical notion of locality. Yet, a
weaker notion of locality, known as no-signalling, survives the no-go-result.
Here, we study its restrictiveness by considering the full set of local quantum
observables. This leads to a much larger set of no-signalling constraints than
usually considered, which is enough to exclude PR-boxes and other types of
super-quantum correlations. We emphasise the close connection with
contextuality, in particular, we show how no-signalling arises naturally from
context composition. Finally, we prove a one-to-one correspondence between
quantum states and collections of (non-signalling) probability distributions
over product contexts under an additional consistency condition between time
arrows in subsystems.
