  We investigate the class of physical theories with the same local structure
as quantum theory, but a potentially different global structure. It has
previously been shown that any bipartite correlations generated by such a
theory must be simulatable in quantum theory, but that this does not hold for
tripartite correlations. Here we explore whether imposing an additional
constraint on this space of theories - that of dynamical reversibility - will
allow us to recover the global quantum structure. In the particular case in
which the local systems are identical qubits, we show that any theory admitting
at least one continuous reversible interaction must be identical to quantum
theory.
