  In the topos approach to quantum theory, the spectral presheaf plays the role
of the state space of a quantum system. We show how a notion of entropy can be
defined within the topos formalism using the equivalence between states and
measures on the spectral presheaf. We show how this construction unifies
Shannon and von Neumann entropy as well as classical and quantum Renyi
entropies. The main result is that from the knowledge of the contextual entropy
of a quantum state of a finite-dimensional system, one can (mathematically)
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.
