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

TL;DR

This paper characterizes Kadison-Schwarz type quantum quadratic operators on 2x2 complex matrices, explores their properties, provides a counterexample, and studies the dynamics of related nonlinear operators on quantum states.

Contribution

It offers a detailed description of Kadison-Schwarz quantum quadratic operators on 2x2 matrices and presents a novel example that is not of this type, along with analyzing their dynamics.

Findings

Provided a description of Kadison-Schwarz quantum quadratic operators on M_2(C)

Constructed an example of a quantum quadratic operator not of Kadison-Schwarz type

Analyzed the dynamics of nonlinear quadratic operators on quantum states

Abstract

In the present paper we study description of Kadison-Schwarz type quantum quadratic operators acting from $\bm_2(\mathbb{C})$ into $\bm_2(\mathbb{C})\o\bm_2(\mathbb{C})$. 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 $\bm_2(\mathbb{C})$.