Separability discrimination and decomposition of m -partite quantum mixed states
Ying Li, Guyan Ni · Physical Review A · 2020
We propose an $E$-truncated $K$-moment and semidefinite relaxations (ETKM-SDR) method to check whether an $m$-partite quantum mixed state is separable and give a decomposition for it if it is. We first convert the separability discrimination problem of mixed states to the positive Hermitian decomposition problem of Hermitian tensors. Then, employing the $E$-truncated $K$-moment method, we obtain an optimization model for discriminating separability. Moreover, by applying the semidefinite relaxation method, we get a hierarchy of semidefinite relaxation optimization models and propose an algorithm for detecting the separability of mixed states. The algorithm can also be used for symmetric and nonsymmetric decomposition of separable mixed states. By numerical examples, we find that not all symmetric separable states have symmetric decompositions.