论文标题
Choi矩阵重新审视
Choi matrices revisited
论文作者
论文摘要
基质代数之间的线性图对应于两个矩阵代数的张量产物中的Choi矩阵，其定义取决于矩阵单元。 Paulsen和Shultz [J。数学。物理。 {\ bf 54}（2013），072201]考虑了一个问题，是否可以在choi矩阵的定义中替换矩阵代数的另一个基础，以保持地图的完全阳性与choi矩阵的阳性之间的对应关系，并根据此基础提供了足够的条件。在本说明中，我们提供了必要和充分的条件，以确保还必须使用Paulsen-Shultz条件。
A linear map between matrix algebras corresponds to the Choi matrix in the tensor product of two matrix algebras, whose definition depends on the matrix units. Paulsen and Shultz [J. Math. Phys. {\bf 54} (2013), 072201] considered the question if one can replace matrix units by another basis of matrix algebras in the definition of Choi matrix to retain the correspondence between complete positivity of maps and positivity of Choi matrices, and gave a sufficient condition on basis under which this is true. In this note, we provide necessary and sufficient conditions, to see that the Paulsen--Shultz condition is also necessary.
