Photonic quantum network transmission assisted by the weak cross-Kerr nonlinearity

Classical network coding permits all internal nodes to encode or decode the incoming messages over proper fields in order to complete a network multicast. Similar quantum encoding scheme cannot be easily followed because of various quantum no-go theorems. In this paper, to avoid these theorems in quantum multiple-source networks, we present a photonic strategy by exploring quantum transferring approaches assisted by the weak cross-Kerr nonlinearity. The internal node may nearly deterministically fuse all incoming photons into a single photon with multiple modes. The fused single photon may be transmitted using two- photonic hyperentanglement as a quantum resource. The quantum splitting as the inverse operation of the quantum fusion allows forwarding quantum states under the quantum no-cloning theorem. Furthermore, quantum addressing schemes are presented to complete the quantum transmissions on multiple-source networks going beyond the classical network broadcasts or quantum n-pair transmissions in terms of their reduced forms.