Quantum protocols at presence of non-abelian superselection rules in the framework of algebraic model

TL;DR

This paper explores how non-abelian superselection rules affect quantum information transfer within an algebraic framework, focusing on the structure of observables and the conditions for successful information coding and retrieval.

Contribution

It introduces a novel algebraic approach to quantum protocols considering non-abelian superselection rules and characterizes conditions for effective quantum information coding.

Findings

Information can be coded using states with projectors in the algebra of observables.

Projectors commuting with the gauge group G enable information recovery.

The algebraic structure of observables influences quantum protocol design.

Abstract

In this paper, we study the influence of non-abelian 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 and, owing to their commutativity with elements of the representation of the group G, they allow the recipient to restore the obtained information