Quantum protocols at presence of nonabelian superselection rules in the framework of algebraic model

Abstract

In this paper, we study the influence of nonabelian superselection rules on the transfer of quantum information with the help of qubits on the base of an algebraic model and formulate quantum protocols. We pay the main attention to the superselection structure of the algebra of observables OG defined by the Cuntz algebra Od (a field algebra) that contains OG as a pointwise fixed subalgebra with respect to the action of the gauge group G. We prove that it is possible to code information only with the help of states such that projectors on them 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.