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Various notions of positivity for bi-linear maps and applications to tri-partite entanglement (1503.05995v1)
Published 20 Mar 2015 in quant-ph and math.OA
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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