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arXiv · 1503.05995

Various notions of positivity for bi-linear maps and applications to tri-partite entanglement

Kyung Hoon Han·Seung-Hyeok Kye
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Abstract

We consider bi-linear analogues of $s$-positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt 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.

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Kyung Hoon Han, Seung-Hyeok Kye. 2015-03-20. Various notions of positivity for bi-linear maps and applications to tri-partite entanglement. https://doi.org/10.1063/1.4931059

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