  We introduce a new notion of entropy for quantum states, called contextual
entropy, and show how it unifies Shannon and von Neumann entropy. The main
result is that from the knowledge of the contextual entropy of a quantum state
of a finite-dimensional system, one can reconstruct the quantum state, i.e.,
the density matrix, if the Hilbert space is of dimension 3 or greater. We
present an explicit algorithm for this state reconstruction and relate our
result to Gleason's theorem.
