Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
Kyung Hoon Han, Seung-Hyeok Kye · Journal of Mathematical Physics · 2015
We consider bi-linear analogues of s-positivity for linear maps. The dual objects of these notions can be described in terms of Schmidt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite versions of Schmidt numbers cover various kinds of bi-separability, and so we may interpret witnesses for those in terms of bi-linear maps. We give concrete examples of witnesses for various kinds of three qubit entanglement.