Decomposable of positive map from M3(C) to M2(M2(C))
Block matrix positive partial transposition
Keywords:
Positive maps, k-positivity, Choi matrix, Completely positivity, Decomposable mapAbstract
In most literature, the decomposition of positive maps from M3 to M2 are discussed where the matrix elements are complex numbers. In this paper we construct a positive maps φ(µ,c1,c2) from M3(C) to M2(M2(C)). The Choi matrices for complete positivity and complete copositivity ares visualized as tensor matrix M3 ⊗M2 with M2(C) as the entry elements. The construction allow us describe decomposability on positive semidefinite matrices.
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References
Arveson W. B. Sub-algebra of C∗-algebra, Acta Math 128(1969), 141-224.
Arveson W. B. Sub-algebra II, Acta Math. 128 (1972), 271-306.
Choi M-D. Completely positive maps on complex matries. Linear Algebra and its applications. 10 (1975), 285-290.
Choi M-D. Positive semidefinite biquadratic Forms. Linear Algebra and its applications. 12 (1975)951005.
Majewski W. A. and Marciniak M. Decomposability of extremal positive unit all maps On M2(C). Quantum Probability Banach Center Publications. 73 (2006 )347-356.
Stinespring W. F. Positive functions on C∗−algebras, Amer. Math. Sot. 6 (1955)211-216.
Stømer E. Decomposablepositive maps on C∗-algebras, Proceedings of the American Mathematical Society. 86 (1982 )402-404,
Stømer E. Positive Linear maps of operator algebra, Acta Math. 110 (1963)233-278.
Stømer E. Positive Linear maps on operator algebra, http://www.springer.com/978-3-642-34368-1. 136(2013)
Tang’ W. On positive linear maps between matrix algebras, Linear Algebra and its Applications. 79 (1986)33-44.
Woronowicz S. L. Positive maps of low dimensional matrix algebras. Rep. Math. Phys. 10 (1976)165183.
Yang Y., Leung D. H. and Tang W. All 2-positive linear maps from M3(C) to M3(C) are decomposable. Linear Algebra and its Applications. 503 (2016) 233-247.
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Copyright (c) 2023 C. A. Winda, Okelo B. Nyaare, Omoke P. M.
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