  A new bound on quantum version of Wielandt inequality for positive (not
necessarily completely positive) maps has been established. Also bounds for
entanglement breaking and PPT channels are put forward which are better bound
than the previous bounds known. We prove that a primitive positive map
$\mathcal{E}$ acting on $\mathcal{M}_d$ that satisfies the Schwarz inequality
becomes strictly positive after at most $2(d-1)^2$ iterations. This is to say,
that after $2(d-1)^2$ iterations, such a map sends every positive semidefinite
matrix to a positive definite one. This finding does not depend on the number
of Kraus operators as the map may not admit any Kraus decomposition. The
motivation of this work is to provide an answer to a question raised in the
article \cite{Wielandt} by Sanz-Garc\'ia-Wolf and Cirac.
