Extreme rays in entangled edge states with positive partial transposes

Kil-Chan Ha

Lin Chen, Dragomir Ž. Djoković

Jinwon Choi, Young‐Hoon Kiem, Seung-Hyeok Kye

We construct a parameterized family of n ⊗ n PPT (positive partial transpose) states of corank one for each n ≥ 3. With a suitable choice of parameters, we show that they are n ⊗ n PPT entangled edge states of corank one for 3 ≤ n ≤ 1000. They violate the range criterion for separability in the most extreme way. Note that corank one is the smallest possible corank for such states. The corank of the partial transpose is given by 2n − 3, which is also the smallest possible corank for the partial transposes of PPT entangled edge states of corank one. They provide the first explicit examples of such states for n ≥ 4.

Kil-Chan Ha, Seung-Hyeok Kye, Young Sung Park

Kil-Chan Ha, Seung-Hyeok Kye

We construct a class of 3 ⊗ 3 entangled edge states with positive partial transposes using indecomposable positive linear maps. This class contains several new types of entangled edge states with respect to the range dimensions of themselves and their partial transposes.

Lieven Clarisse