  The Schmidt number is a fundamental parameter characterizing the properties
of quantum states, and the local projections are a fundamental operation in
quantum physics. We investigate the relation between the Schmidt numbers of
bipartite states and their projected states. We show that there exist bipartite
positive-partial-transpose (PPT) entangled states of any given Schmidt number.
We further construct the notion of joint Schmidt number for multipartite
states, and its relation with the Schmidt number of bipartite reduced density
operators.
