On equality of complete positivity and complete copositivity of positive map

Subject Areas : Operator theory

C. A.  Winda ¹ (Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya)
N. B.  Okelo ² (Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya)
O.  Ongati ³ (Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Kenya)

Received: 2022-01-08 Accepted : 2022-05-30 Published : 2022-06-01

Keywords: 2-positivity, Choi matrix, completely positivity,

Abstract :

‎In this paper we construct a $2$-positive map from $\ma_4(\Complex)$ to $\ma_5(\Complex)$ and state the conditions under which the map is positive and completely positive (copositivity of positive)‎. ‎The construction allows us to create a decomposable map, where the Choi matrix of complete positivity is equal to the Choi matrix of complete copositivity‎.

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