Representation of the probability distribution used in the definition of quantum logical entropy. Any state ρ, together with a partition characterized by a PVM, which is associated with an orthonormal basis in the corresponding Hilbert space, defines a probability distribution. This is the case even in case of coarse (i.e., degenerate) PVMs, as illustrated by the yellow partition. These distributions allow the introduction of (PVM-dependent) logical entropies for quantum systems.