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

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 $\bm_2(\mathbb{C})$.

14 pages. arXiv admin note: text overlap with arXiv:0902.4500

References in corpus (3)

• On ergodic properties of convolution operators associated with compact quantum groups
• On non-completely positive quantum dynamical maps on spin chains
• On description of bistochastic Kadison-Schwarz operators on M_2(C)