Deterministic quantum state transfer between remote atoms with photon-number superposition states

We propose a protocol for quantum networking based on deterministic quantum state transfer between distant memory nodes using photon-number superposition states (PNSS). In the suggested scheme, the quantum nodes are single atoms confined in high-finesse optical cavities linked by photonic channels. The quantum information written in a superposition of atomic Zeeman states of sending system is faithfully mapped through cavity-assisted Raman scattering onto PNSS of linearly polarized cavity photons. The photons travel to the receiving cavity, where they are coherently absorbed with unit probability creating the same superposition state of the second atom, thus ensuring high-fidelity transfer between distant nodes. We develop this approach at first for photonic qubit and show that this superposition state is no less reliably protected against the propagation losses compared to the single-photon polarization states, whereas the limitation associated with the delivery of more than one photon does not affect the process fidelity. Then, by preserving the advantages of qubits, we extend the developed technique to the case of state transfer by photonic qutrit, which evidently possesses more information capacity. This reliable and efficient scheme promises also a successful distribution of entanglement over long distances in quantum networks.