All reversible dynamics in maximally nonlocal theories are trivial

A remarkable feature of quantum theory is nonlocality (Bell inequality violations). However, quantum correlations are not maximally nonlocal, and it is natural to ask whether there are compelling reasons for rejecting theories in which stronger violations are possible. To shed light on this question, we consider post-quantum theories in which maximally nonlocal states (nonlocal boxes) occur. We show that reversible transformations in such theories are trivial: they consist solely of local operations and permutations of systems. In particular, no correlations can be created; nonlocal boxes cannot be prepared from product states and classical computers can efficiently simulate all such processes.