  We show that the Entropy Photon-Number Inequality (EPnI) holds where one of
the input states is the vacuum state and for several candidates of the other
input state that includes the cases when the state has the eigenvectors as the
number states and either has only two non-zero eigenvalues or has arbitrary
number of non-zero eigenvalues but is a high entropy state. We also discuss the
conditions, which if satisfied, would lead to an extension of these results.
