  It is well-known that von Neumann entropy is nonmonotonic unlike Shannon
entropy (which is monotonically nondecreasing). Consequently, it is difficult
to relate the entropies of the subsystems of a given quantum state. In this
paper, we show that if we consider quantum secret sharing states arising from a
class of monotone span programs, then we can partially recover the monotonicity
of entropy for the so-called unauthorized sets. Furthermore, we can show for
these quantum states the entropy of the authorized sets is monotonically
nonincreasing.
