Mapping-reduction hardness of the quantum separability problem

Determine whether the quantum separability problem—deciding if a bipartite density operator is separable—is NP-hard with respect to polynomial-time mapping (Karp) reductions.

Background

While separability testing is known to be NP-hard under various settings, the authors state that the question of NP-hardness under polynomial-time mapping reductions remains open, paralleling the mapping-reduction hardness question for mixed-unitary detection.

This underscores a broader uncertainty regarding the strongest reducibility form in which separability testing retains NP-hardness.