  Generalized probabilistic theories (GPTs) provide a framework in which a
range of possible theories can be examined, including classical theory, quantum
theory and those beyond. In general, enlarging the state space of a GPT leads
to fewer possible measurements because the additional states give stronger
constraints on the set of effects, the constituents of measurements. This can
have implications for information processing. In boxworld, for example, a GPT
in which any no-signalling distribution can be realised, there is no analogue
of a measurement in the Bell basis and hence the analogue of entanglement
swapping is impossible. A comprehensive study of measurements on multiple
systems in boxworld has been lacking. Here we consider such measurements in
detail, distinguishing those that can be performed by interacting with
individual systems sequentially (termed wirings), and the more interesting set
of those that cannot. We compute all the possible boxworld effects for cases
with small numbers of inputs, outputs and parties, identifying those that are
wirings. The large state space of boxworld leads to a small effect space and
hence the effects of boxworld are widely applicable in GPTs. We also show some
possible uses of non-wirings for information processing by studying state
discrimination, nonlocality distillation and the boxworld analogue of
nonlocality without entanglement. Finally, we connect our results to the study
of logically consistent classical processes and to the composition of
contextuality scenarios. By enhancing understanding of measurements in
boxworld, our results could be useful in studies of possible underlying
principles on which quantum theory can be based.
