On Kadison-Schwarz Type Quantum Quadratic Operators on 𝕄 2 ℂ

Abstract

We study the description of Kadison-Schwarz type quantum quadratic operators (q.q.o.) acting from ${𝕄}_2\left(ℂ\right)$ into ${𝕄}_{\mathrm{2}}(ℂ)\otimes {𝕄}_{\mathrm{2}}(ℂ)$. Note that such kind of operators is a generalization of quantum convolution. By means of such a description we provide an example of q.q.o. which is not a Kadison-Schwartz operator. Moreover, we study dynamics of an associated nonlinear (i.e., quadratic) operators acting on the state space of ${𝕄}_2\left(ℂ\right)$.