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Generalized probabilistic theories (GPTs) provide a framework in which arange of possible theories can be examined, including classical theory, quantumtheory and those beyond. In general, enlarging the state space of a GPT leadsto fewer possible measurements because the additional states give strongerconstraints on the set of effects, the constituents of measurements. This canhave implications for information processing. In boxworld, for example, a GPTin which any no-signalling distribution can be realised, there is no analogueof a measurement in the Bell basis and hence the analogue of entanglementswapping is impossible. A comprehensive study of measurements on multiplesystems in boxworld has been lacking. Here we consider such measurements indetail, distinguishing those that can be performed by interacting withindividual systems sequentially (termed wirings), and the more interesting setof those that cannot. We compute all the possible boxworld effects for caseswith small numbers of inputs, outputs and parties, identifying those that arewirings. The large state space of boxworld leads to a small effect space andhence the effects of boxworld are widely applicable in GPTs. We also show somepossible uses of non-wirings for information processing by studying statediscrimination, nonlocality distillation and the boxworld analogue ofnonlocality without entanglement. Finally, we connect our results to the studyof logically consistent classical processes and to the composition ofcontextuality scenarios. By enhancing understanding of measurements inboxworld, our results could be useful in studies of possible underlyingprinciples on which quantum theory can be based.

Multi-system measurements in generalized probabilistic theories and their role in information processing