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We investigate the class of physical theories with the same local structureas quantum theory, but a potentially different global structure. It haspreviously been shown that any bipartite correlations generated by such atheory must be simulatable in quantum theory, but that this does not hold fortripartite correlations. Here we explore whether imposing an additionalconstraint on this space of theories - that of dynamical reversibility - willallow us to recover the global quantum structure. In the particular case inwhich the local systems are identical qubits, we show that any theory admittingat least one continuous reversible interaction must be identical to quantumtheory.

Deriving quantum theory from its local structure and reversibility