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Motivated by the desire to better understand the class of quantum operationson bipartite systems that preserve positivity of partial transpose (PPToperations) and its relation to the class LOCC (local operations and classicalcommunication), we present some results on deterministic bipartite pure statetransformations by PPT operations. Restricting our attention to the case wherewe start with a rank K maximally entangled state, we give a necessary conditionfor transforming it into a given pure state, which we show is also sufficientwhen K is two and the final state has Schmidt rank three. We show that it issufficient for all K and all final states provided a conjecture about a certainfamily of semidefinite programs is true. We also demonstrate that thephenomenon of catalysis can occur under PPT operations and that, unlike LOCCcatalysis, a maximally entangled state can be a catalyst. Finally, we give anecessary and sufficient condition for the possibility of transforming a rank Kmaximally entangled state to an arbitrary pure state by PPT operations assistedby some maximally entangled catalyst.

Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose