Locally Tomographic Shadows (Extended Abstract)

Given a monoidal probabilistic theory — a symmetric monoidal category C of systems and processes, together with a functor V assigning concrete probabilistic models to objects of C — we construct a locally tomographic probabilistic theory LT(C,V) — the locally tomographic shadow of (C, V) — describing phenomena observable by local agents controlling systems in C, and able to pool information about joint measurements made on those systems. Some globally distinct states become locally indistinguishable in LT(C,V), and we restrict the set of processes to those that respect this indistinguishability. This construction is investigated in some detail for real quantum theory.