Choi matrices revisited. II

• URL: http://arxiv.org/abs/2307.09247v3
• Date: Thu, 12 Oct 2023 04:01:18 GMT
• Title: Choi matrices revisited. II
• Authors: Kyung Hoon Han, Seung-Hyeok Kye
• Abstract summary: We consider all possible variants of Choi matrices of linear maps. We show that they are determined by non-degenerate bilinear forms on the domain space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between $k$-superpositivity and Schmidt number $\le k$ as well as $k$-positivity and $k$-block-positivity. We also compare de Pillis' definition [Pacific J. Math. 23 (1967), 129--137] and Choi's definition [Linear Alg. Appl. 10 (1975), 285--290], which arise from different bilinear forms.

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