  We exhibit infinitely many new, constrained inequalities for the von Neumann
entropy, and show that they are independent of each other and the known
inequalities obeyed by the von Neumann entropy (basically strong
subadditivity). The new inequalities were proved originally by Makarychev et
al. [Commun. Inf. Syst., 2(2):147-166, 2002] for the Shannon entropy, using
properties of probability distributions. Our approach extends the proof of the
inequalities to the quantum domain, and includes their independence for the
quantum and also the classical cases.
