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

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

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...

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Main Author:	Mukhamedov, Farrukh
Format:	Article
Language:	English
Published:	World Scientific 2015
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/47383/1/02Mukhamedov.pdf http://irep.iium.edu.my/47383/
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spelling	my.iium.irep.473832016-07-21T00:04:53Z http://irep.iium.edu.my/47383/ On pure quasi-quantum quadratic operators of of M2(C) II Mukhamedov, Farrukh QA Mathematics 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. World Scientific 2015 Article REM application/pdf en http://irep.iium.edu.my/47383/1/02Mukhamedov.pdf 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 10.1142/S1230161215500249
institution	Universiti Islam Antarabangsa Malaysia
building	IIUM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	International Islamic University Malaysia
content_source	IIUM Repository (IREP)
url_provider	http://irep.iium.edu.my/
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, Farrukh On pure quasi-quantum quadratic operators of of M2(C) II
description	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.
format	Article
author	Mukhamedov, Farrukh
author_facet	Mukhamedov, Farrukh
author_sort	Mukhamedov, Farrukh
title	On pure quasi-quantum quadratic operators of of M2(C) II
title_short	On pure quasi-quantum quadratic operators of of M2(C) II
title_full	On pure quasi-quantum quadratic operators of of M2(C) II
title_fullStr	On pure quasi-quantum quadratic operators of of M2(C) II
title_full_unstemmed	On pure quasi-quantum quadratic operators of of M2(C) II
title_sort	on pure quasi-quantum quadratic operators of of m2(c) ii
publisher	World Scientific
publishDate	2015
url	http://irep.iium.edu.my/47383/1/02Mukhamedov.pdf http://irep.iium.edu.my/47383/
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score	13.211869

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

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