Halos and undecidability of tensor stable positive maps

van der Eyden, Mirte; Netzer, Tim; Cuevas, Gemma de las

doi:http://dx.doi.org/10.1088/1751-8121/ac726e

Halos and undecidability of tensor stable positive maps

License

Citation

van der Eyden M, Netzer T, de las Cuevas G. Halos and undecidability of tensor stable positive maps. J Phys A Math Theor. 2022 Jul 1;55(26):264006. DOI: 10.1088/1751-8121/ac726e

Abstract

A map P is tensor stable positive (tsp) if P⊗n is positive for all n, and essential tsp if it is not completely positive or completely co-positive. Are there essential tsp maps? Here we prove that there exist essential tsp maps on the hypercomplex numbers. It follows that there exist bound entangled states with a negative partial transpose (NPT) on the hypercomplex, that is, there exists NPT bound entanglement in the halo of quantum states. We also prove that tensor stable positivity on the matrix multiplication tensor is undecidable, and conjecture that tensor stable positivity is undecidable. Proving this conjecture would imply existence of essential tsp maps, and hence of NPT bound entangled states.