  A common misconception is that decoherence gives the eigenstates that we
observe to be fairly definite about a subsystem (e.g., approximate eigenstates
of position) as the elements of the Schmidt basis in which the density matrix
of the subsystem is diagonal. Here I show that in simple examples of linear
systems with gaussian states, the Schmidt basis states have as much mean
uncertainty about position as the full density matrix with its combination of
different possibilities.
