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Hexagonal boron nitride exhibits two types of defects with great potentialfor quantum information technologies: single-photon emitters (SPEs) andone-dimensional grain boundaries hosting topologically-protected phonons,termed as {\it{topologically-protected phonon lines}} (TPL). Here, by means ofa simple effective model and density functional theory calculations, we showthat it is possible to use these phonons for the transmission of information.Particularly, a single SPE can be used to induce single-, two- and qubit-phononstates in the one dimensional channel, and \textit{(ii)} two distant SPEs canbe coupled by the TPL that acts as a waveguide, thus exhibiting strong quantumcorrelations. We highlight the possibilities offered by this material-built-innano-architecture as a phononic device for quantum information technologies.

Generation of phonon quantum states and quantum correlations among single photon emitters in hexagonal boron nitride