Joint measurements in boxworld and their role in information processing

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Abstract
Boxworld is a theory in which any no-signalling distribution can be realised. It hence has more nonlocality than quantum theory, enhancing certain information processing tasks. However, this richness in correlations necessarily leads to a poorer set of possible measurements -- for example, there is no analogue of a Bell basis measurement in boxworld 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. We then show some possible uses of non-wirings for information processing by studying state discrimination, nonlocality distillation and the boxworld analogue of nonlocality without entanglement. 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.

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