Aplicações do teorema de Sinkhorn - Knopp ao emaranhamento quântico - Rodríguez, John Alexander Mora (2022)
The separability problem asks for a deterministic criterion for distinguishing those quantum states that are entangled from those that are not (separable states). This problem was solved just for states $γ \in M_k \otimes M_m$ with $km≤ 6$. For k,m arbitrary, it is already known that this problem is NP-hard. In this work, we present the solution to the problem for states in $M_2 \otimes M_2$ as an application of the Sinkhorn-Knopp Theorem for positive maps. In addition, we show that the separability problem in $M_2 \otimes M_n$ can be reduced to states in the filter normal form.