Algebraic Model of Non-Abelian Superselection Rules Considering Conjugate Endomorphism
A. S. Nikitin, A. S. Sitdikov · Lobachevskii Journal of Mathematics · 2024
In this paper, we consider an extension of the previously proposed algebraic model and study the constraints of non-Abelian superselection rules on the transfer quantum information, taking into account conjugate endomorphism. The procedure of averaging (over the group $$G=SU(3)$$ ) projectors to the basic states of coherent orthogonal subspaces into which the space of two three-level systems decomposes is considered. Main attention is paid 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 to the action of the gauge group $$G$$ . As an application of the model, we consider the encoding of information using a three-level system and show that information can be transmitted only by those states whose projectors belong to the algebra of observables. These projectors commute with the elements of the representation of the group $$G$$ , and therefore, allow the recipient to restore the obtained information.