  Ultrafast electron diffraction and time-resolved serial crystallography are
the basis of the ongoing revolution in capturing at the atomic level of detail
the structural dynamics of molecules. However, most experiments employ the
classical "ball-and-stick" depictions, and the information of molecular quantum
states, such as the density matrix, is missing. Here, we introduce a framework
for the preparation and ultrafast coherent diffraction from rotational wave
packets of molecules, and we establish a new variant of quantum state
tomography for ultrafast electron diffraction to characterize the molecular
quantum states. The ability to reconstruct the density matrix of molecules of
arbitrary degrees of freedom will provide us with an unprecedentedly clear view
of the quantum states of molecules, and enable the visualization of effects
dictated by the quantum dynamics of molecules.
