Mapping-reduction hardness of mixed-unitary detection

Determine whether the mixed-unitary detection promise problem is NP-hard with respect to polynomial-time mapping (Karp) reductions, rather than only via polynomial-time Turing reductions.

Background

The main result shows mixed-unitary detection is strongly NP-hard under polynomial-time Turing reductions. Whether this hardness can be strengthened to NP-hardness under polynomial-time mapping (Karp) reductions remains unproven.

The authors point out that a similar question is open for the quantum separability problem, highlighting a broader gap between known Turing-reduction hardness and mapping-reduction hardness in quantum information decision problems.