Entanglement Percolation In Quantum Small-world Networks With The Mixed States

We study entanglement percolation in the mixed-state small-world networks by generating function and entanglement swapping.Through theoretical calculation and numerical simulation,the relationship between normalized average component size and path length in small-world networks is analyzed,and we find that the average component size is larger under the shorter path in the small-world network.Similarly,quantum small-world networks have high aggregation and short path.It's further discovered that the average component size is advanced with the increasing of fidelity.In addition,we can debase the fidelity needed in the information dissemination by enlarging average degree in quantum small-world networks.At last,fidelity can be improved with the help of entanglement swapping,indicating that hat entanglement swapping can optimize the entanglement percolation in quantum small-world networks.Firstly,we build up a quantum small-world network model.Compared to classical small-world networks,nodes in a quantum small-world network can be regarded as quantum repeaters,which can store,deal with and transmit quantum information.The key to quantum information dissemination is to make entangled states of long distance teleportation.Because of the influence of noise and de-coherence in the process of making and transferring,quantum states will grow into mixed entangled states.Taking this into account,we deliver the information passage for mixed entangled states between any two nodes in quantum small-world networks.If we obtain maximally entangled states from mixed entangled ones with certain probability,entanglement percolation can bee realized.The relationship between average component size and path length is analyzedin different network models.Based on theoretical calculation and numerical simulation,it's found that the average component size is larger under the same path in quantum small-world networks.Namely,almost nodes can be connected together,and information transferring can be achieved.In the process of information dissemination remotely,the requirements for singlet fidelity obtained from mixed states are higher with the concentration of path length increasing.We study the relationship between average component size and singlet fidelity in quantum small-world networks through numerical simulation,finding that average component size is also growing as singlet fidelity adds,but the giant connected component remains still.It's further discovered that you can change the top structure of the network by changing its average degrees,resulting in lowering singlet fidelity in information remote communication.Finally,singlet fidelity can be changed with the help of quantum operations.By adjusting the parameter in quantum states to some specific values,singlet fidelity can be advanced,indicating that entanglement swapping can optimize entanglement percolation in quantum small-world networks.