In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, emphasis mine):
So, one is now faced with the problem similar to the initial one, i.e., are the inseparable states with positive partial transposition nonlocal?
In other words, the question is whether inseparable states which have a positive partial transpose can (or must?) exhibit nonlocal correlations.
This was an open question in 1998. Has it been answered in the meantime, or were there developments in this direction?