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arXiv · 1211.3511

On Kadison-Schwarz type quantum quadratic operators on $\bm_2(\mathbb{C})$

Farrukh Mukhamedov·Abduaziz Abduganiev
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Abstract

In the present paper we study description of Kadison-Schwarz type quantum quadratic operators acting from $\bm_2(\mathbb{C})$ into $\bm_2(\mathbb{C})ø\bm_2(\mathbb{C})$. Note that such kind of operator is a generalization of quantum convolution. By means of such a description we provide an example of q.q.o. which is not a Kadision-Schwartz operator. Moreover, we study dynamics of an associated nonlinear (i.e. quadratic) operators acting on the state space of $\bm_2(\mathbb{C})$.

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Farrukh Mukhamedov, Abduaziz Abduganiev. 2013-04-20. On Kadison-Schwarz type quantum quadratic operators on $\bm_2(\mathbb{C})$. https://doi.org/10.1155/2013%2F278606

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