Second-level termination of the PPT entanglement-cost hierarchy for two qutrits

arXiv:2611.12993v1 Announce Type: new Abstract: We prove that for arbitrary two-qutrit quantum states, the semidefinite programming lower-bound hierarchy for the PPT entanglement cost terminates at the second level. Therefore, under operations preserving positive partial transpose, its zero-error asymptotic entanglement cost can be obtained by a semidefinite program involving only three Hermitian matrix variables. The key to the proof is to shorten the feasible dual chain by one level; to this end, we combine finite certificates verified by exact rational arithmetic with analytic estimates near the boundary of the parameter domain. This result shows that a unified terminating level exists for two-qutrit systems, whereas no unified terminating level exists for all dimensions.