Choi matrices revisited. III

• URL: http://arxiv.org/abs/2410.13120v1
• Date: Thu, 17 Oct 2024 01:18:35 GMT
• Title: Choi matrices revisited. III
• Authors: Kyung Hoon Han, Seung-Hyeok Kye,
• Abstract summary: We look for all linear isomorphisms from the mapping spaces onto the tensor products of matrices. They 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.
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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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