Converse implication from NPPT bound entanglement to tensor-stable positive maps

Ascertain whether the existence of NPPT bound-entangled states implies the existence of non-trivial tensor-stable positive maps, i.e., positive maps P for which P^{⊗n} is positive for all n ≥ 1 but P is neither completely positive nor completely co-positive.

Background

The authors prove that if a non-trivial tensor-stable positive map exists, then NPPT bound-entangled states exist. This establishes a one-way implication connecting map positivity under tensor powers to a key open problem in entanglement theory.

They explicitly pose the converse direction as open: whether the existence of NPPT bound entanglement guarantees the existence of non-trivial tensor-stable positive maps. Resolving this would yield a bidirectional equivalence and deepen the structural understanding of positivity and entanglement.