Relation between the entropy and the linear entropy in the ion–laser interaction

Abstract

It is shown that, in the interaction of a field and a qubit, there exists a relation between the linear entropy and the von Neumann entropy. The Cayley–Hamilton theorem is used to obtain such relation. In the case we study, the qubit is given by the internal degrees of freedom of an ion trapped in a Paul trap and the field given by its external (vibrational) degrees of freedom.