Entangled states with a positive partial transpose (so-called PPT states) are
central to many interesting problems in quantum theory. On one hand, they are
considered to be weakly entangled, since no pure state entanglement can be
distilled from them. On the other hand, it has been shown recently that some of
these PPT states exhibit genuinely high-dimensional entanglement, i.e. they
have a high Schmidt number. Here we investigate d×d dimensional PPT
states for d≥4 discussed recently by Sindici and Piani, and by
generalizing their methods to the calculation of Schmidt numbers we show that a
linear d/2 scaling of its Schmidt number in the local dimension d can be
attained.Comment: 8 page