  Quantum theory has the property of "local tomography": the state of any
composite system can be reconstructed from the statistics of measurements on
the individual components. In this respect the holism of quantum theory is
limited. We consider in this paper a class of theories more holistic than
quantum theory in that they are constrained only by "bilocal tomography": the
state of any composite system is determined by the statistics of measurements
on pairs of components. Under a few auxiliary assumptions, we derive certain
general features of such theories. In particular, we show how the number of
state parameters can depend on the number of perfectly distinguishable states.
We also show that real-vector-space quantum theory, while not locally
tomographic, is bilocally tomographic.
