The asymptotic lift of a completely positive map
نویسندگان
چکیده
منابع مشابه
The Asymptotic Lift of a Completely Positive Map
Starting with a unit-preserving normal completely positive map L : M → M acting on a von Neumann algebra or more generally a dual operator system we show that there is a unique reversible system α : N → N (i.e., a complete order automorphism α of a dual operator system N) that captures all of the asymptotic behavior of L, called the asymptotic lift of L. This provides a noncommutative generaliz...
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We show that for every “locally finite” unit-preserving completely positive map P acting on a C∗-algebra, there is a corresponding ∗-automorphism α of another unital C∗-algebra such that the two sequences P, P , P , . . . and α,α, α, . . . have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps o...
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For a linear map from Mm to Mn, besides the usual positivity, there are two stronger notions, complete positivity and super-positivity. Given a positive linear map φ we study a decomposition φ = φ − φ with completely positive linear maps φ (j = 1, 2). Here φ + φ is of simple form with norm small as possible. The same problem is discussed with superpositivity in place of complete positivity.
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Using a bordering approach, and building upon an already known factorization of a principal block, we establish sufficient conditions under which we can extend this factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions.
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We investigate the set a) of positive, trace preserving maps acting on density matrices of size N , and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose positive partial transpose and e) are superpositive. Working with the Hilbert-Schmidt (Euclidean) measure we derive tight explicit two-sided bounds for the volu...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2007
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2006.11.014