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arXiv · 2410.13120

Choi matrices revisited. III

Kyung Hoon Han·Seung-Hyeok Kye
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Abstract

We look for all linear isomorphisms from the mapping spaces onto the tensor products of matrices which send $k$-superpositive maps onto unnormalized bi-partite states of Schmidt numbers less than or equal to $k$. They also send $k$-positive maps onto $k$-block-positive matrices. We also look for all the bilinear pairings between the mapping spaces and tensor products of matrices which retain the usual duality between $k$-positivity and Schmidt numbers $\le k$. They also retain the duality between $k$-superpositivity and $k$-block-positivity.

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Kyung Hoon Han, Seung-Hyeok Kye. 2024-10-17. Choi matrices revisited. III. https://arxiv.org/abs/2410.13120

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