1205.2902 (Lin Chen et al.)

Equivalence classes and canonical forms for two-qutrit entangled states
of rank four having positive partial transpose    [PDF]

Lin Chen, Dragomir Z. Djokovic

We show that the set of SLOCC equivalence classes of non-normalized two-qutrit entangled states of rank four with positive partial transpose (PPT), equipped with the quotient topology, is homeomorphic to the quotient, R/A_5, of an open rectangular four-dimensional box R by the action of the alternating group A_5. We also show that any two-qutrit PPT entangled state of rank four can be converted by invertible local operations into the canonical form depending on four positive parameters a,b,c,d. In particular, all checkerboard PPT entangled states can be parametrized by only two real parameters. We also summarize the known results on two-qutrit extreme and edge PPT states, and construct additional examples of such states.

View original: http://arxiv.org/abs/1205.2902