Abstract
In this paper, we consider an extension of the previously proposedalgebraic model and study the constraints of non-Abeliansuperselection rules on the transfer quantum information, takinginto account conjugate endomorphism. The procedure of averaging(over the group \(G=SU(3)\) ) projectors to the basic states ofcoherent orthogonal subspaces into which the space of twothree-level systems decomposes is considered. Main attention ispaid to the superselection structure of the algebra of observables \({}^{0}O_{G}\) defined by the Cuntz algebra \({}^{0}O_{d=3}\) (field algebra)containing \({}^{0}O_{G}\) as a pointwise fixed subalgebra with respect tothe action of the gauge group \(G\) . As an application of the model,we consider the encoding of information using a three-level systemand show that information can be transmitted only by those stateswhose projectors belong to the algebra of observables. Theseprojectors commute with the elements of the representation of thegroup \(G\) , and therefore, allow the recipient to restore theobtained information.
