  Motivated by the desire to better understand the class of quantum operations
on bipartite systems that preserve positivity of partial transpose (PPT
operations) and its relation to the class LOCC (local operations and classical
communication), we present some results on deterministic bipartite pure state
transformations by PPT operations. Restricting our attention to the case where
we start with a rank K maximally entangled state, we give a necessary condition
for transforming it into a given pure state, which we show is also sufficient
when K is two and the final state has Schmidt rank three. We show that it is
sufficient for all K and all final states provided a conjecture about a certain
family of semidefinite programs is true. We also demonstrate that the
phenomenon of catalysis can occur under PPT operations and that, unlike LOCC
catalysis, a maximally entangled state can be a catalyst. Finally, we give a
necessary and sufficient condition for the possibility of transforming a rank K
maximally entangled state to an arbitrary pure state by PPT operations assisted
by some maximally entangled catalyst.
