On pure quasi-quantum quadratic operators of of M2(C) II

Mukhamedov, Farrukh (2015) On pure quasi-quantum quadratic operators of of M2(C) II. Open Systems & Information Dynamics, 22 (4). pp. 1-22. ISSN 1230-1612

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Abstract

In the present paper we study quasi quantum quadratic operators (QQO) acting on the algebra of 2 × 2 matrices M2(C). We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in R 3. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO. in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.

Item Type:	Article (Journal)
Additional Information:	5537/47383
Uncontrolled Keywords:	separability; algebras; spheres; states maps
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	08 Jan 2016 14:57
Last Modified:	21 Jul 2016 08:04
URI:	http://irep.iium.edu.my/id/eprint/47383

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