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

TL;DR

This paper investigates pure-state transformations and catalysis under PPT operations, providing conditions for state conversion, demonstrating catalysis possibilities, and exploring the relation to LOCC operations in bipartite quantum systems.

Contribution

It offers new necessary and sufficient conditions for pure state transformations under PPT operations, including catalysis, and discusses the relation to LOCC.

Findings

Necessary conditions for transforming rank K maximally entangled states.

Catalysis can occur under PPT operations, including with maximally entangled catalysts.

Conditions for pure state transformations with PPT catalysis are established.

Abstract

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.