  With the ability to directly obtain the Wigner function and density matrix of
photon states, quantum tomography (QT) has had a significant impact on quantum
optics, quantum computing and quantum information. By an appropriate sequence
of measurements on the evolution of each degreeof freedom (DOF), the full
quantum state of the observed photonic system can be determined. The first
proposal to extend the application of QT to reconstruction of complete quantum
states of matter wavepackets had generated enormous interest in ultrafast
diffraction imaging and pump-probe spectroscopy of molecules. This interest was
elevated with the advent of ultrafast electron and X-ray diffraction techniques
using electron accelerators and X-ray free electron lasers to add temporal
resolution to the observed nuclear and electron distributions. However, the
great interest in this area has been tempered by the illustration of an
impossibility theorem, known as the dimension problem. Not being able to
associate unitary evolution to every DOF of molecular motion, quantum
tomography could not be used beyond 1D and categorically excludes most
vibrational and all rotational motion of molecules. Here we present a
theoretical advance to overcome the notorious dimension problem. Solving this
challenging problem is important to push imaging molecular dynamics to the
quantum limit. The new theory has solved this problem, which makes quantum
tomography a truly useful methodology in ultrafast physics and enables the
making of quantum version of a molecular movie. With the new theory, quantum
tomography can be finally advanced to a sufficient level to become a general
method for reconstructing quantum states of matter, without being limited in
one dimension. Our new concept is demonstrated using a simulated dataset of
ultrafast diffraction experiment of laser-aligned nitrogen molecules.
