  The quantum de Finetti theorem says that, given a symmetric state, the state
obtained by tracing out some of its subsystems approximates a convex sum of
power states. The more subsystems are traced out, the better this approximation
becomes. Schur-Weyl duality suggests that there ought to be a dual result that
applies to a unitarily invariant state rather than a symmetric state. Instead
of tracing out a number of subsystems, one traces out part of every subsystem.
The theorem then asserts that the resulting state approximates the fully mixed
state, and the larger the dimension of the traced-out part of each subsystem,
the better this approximation becomes. This paper gives a number of
propositions together with their dual versions, to show how far the duality
holds.
