Positive maps that are not completely positive
نویسندگان
چکیده
منابع مشابه
Gluing of completely positive maps
Gluings of completely positive maps (CPMs) are defined and investigated. As a brief description of this concept consider a pair of ‘evolution machines’, each with the ability to evolve the internal state of a ‘particle’ inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the ou...
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Given commuting families of Hermitian matrices {A1, . . . , Ak} and {B1, . . . , Bk}, conditions for the existence of a completely positive map Φ, such that Φ(Aj) = Bj for j = 1, . . . , k, are studied. Additional properties such as unital or / and trace preserving on the map Φ are also considered. Connections of the study to dilation theory, matrix inequalities, unitary orbits, and quantum inf...
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Characterizations are given for the positive and completely positive maps on n n complex matrices that leave invariant the diagonal entries or the kth elementary symmetric function of the diagonal entries, 1 < k n. In addition, it was shown that such a positive map is always decomposable if n 3, and this fails to hold if n > 3. The real case is also considered.
متن کاملModeling heat transport through completely positive maps.
We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate quantum master equations. The standard microscopic derivation of the weak-coupling Lindblad equation in the secular approximation is considered, and shown to be ...
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We consider the completely positive map on the Toeplitz operator system given by conjugation by a composition operator; that is, we analyze operators of the form C∗ φTfCφ We prove that every such operator is weakly asymptotically Toeplitz, and compute its asymptotic symbol in terms of the Aleksandrov-Clark measures for φ. When φ is an inner function, this operator is Toeplitz, and we show under...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2000
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.62.024302