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Characterization of Maps on Positive Semidefinite Choi Matrices

C. A. Winda, Benard Okelo, Omolo Ongati

Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study, we have described the structure of the Choi matrices for 2-positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps from n to n+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive maps ф from Mn to Mn + 1(2 ≥ 2) between matrix algebras.Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study, we have described the structure of the Choi matrices for 2-positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps from n to n+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive maps ф from Mn to Mn + 1(2 ≥ 2) between matrix algebras.

MathLAB JournalAug 31, 20200 citations

Positive Maps and Entanglement in Real Hilbert Spaces

Giulio Chiribella, Kenneth R. Davidson, Vern I. Paulsen +1 more

arXiv:2207.02510Annales Henri PoincaréMay 24, 202319 citations

Choi matrices revisited

Seung-Hyeok Kye

A linear map between matrix algebras corresponds to the Choi matrix in the tensor product of two matrix algebras whose definition depends on matrix units. Paulsen and Shultz [J. Math. Phys. 54, 072201 (2013)] considered the question if one can replace matrix units by another basis of matrix algebras in the definition of the Choi matrix to retain the correspondence between the complete positivity of maps and the 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.A linear map between matrix algebras corresponds to the Choi matrix in the tensor product of two matrix algebras whose definition depends on matrix units. Paulsen and Shultz [J. Math. Phys. 54, 072201 (2013)] considered the question if one can replace matrix units by another basis of matrix algebras in the definition of the Choi matrix to retain the correspondence between the complete positivity of maps and the 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.

arXiv:2206.09324Journal of Mathematical PhysicsSep 1, 20225 citations

Generalized Choi-Kraus dilations of linear maps between matrix algebras

Deguang Han, Qianf ng Hu, Rui Liu

Operators and MatricesJan 1, 20221 citation

Exposedness of elementary positive maps between matrix algebras

Seung-Hyeok Kye

The positive linear maps Ads which send matrices x to s∗xs play important roles in quantum information theory as well as matrix theory. It was proved by [Marciniak M. Rank properties of exposed positive maps. Linear Multilinear Alg. 2013;61:970–975] that the map Ads generates an exposed ray of the convex cone of all positive linear maps. In this note, we provide two alternative proofs, using Choi matrices and Woronowicz's method, respectively.

arXiv:2301.05788Linear and Multilinear AlgebraJan 18, 20242 citations

POSITIVE MAPS AND SEPARABLE STATES IN MATRIX ALGEBRAS

Andrzej Kossakowski

Mar 1, 20060 citations

Choi matrices, norms and entanglement associated with positive maps on matrix algebras

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