Quantum Entanglement Percolation In Complex Networks

With the rapid development of quantum information science, the investigations ofpractical application of quantum communication and quantum computation haveattracted much attention in recent years. The qubits in quantum communication andquantum computation need to be transmitted in a quantum network. The major point ofthe wide range realization of quantum network is the long distance establishment ofquantum entanglement. In this article, we theoretically study the preparation oflong-distance quantum entanglement in small-world networks.Due to the effects of decoherence of quantum states, the noise in the environment,and etc., the entangled quantum states can be easily disturbed and quickly attenuatedwhen the distance of transferring quantum states is increased. To deal with theattenuation of entangled states in long distance transmission, the concepts of “quantumrepeater” and “quantum network” were introduced. In a quantum network, the quantumrepeaters supply amplification and storage for remote quantum states. The repeater isconsidered as one node, and one or more pairs of partially entangled states sharingbetween two nodes are considered as edges. With probability (singlet convertprobability), the partially entangled states could be converted into maximally entangledstates and then the quantum channel between two nodes is established. If the preparationand transmission of entangled quantum states can be realized for any remote nodes, thesenodes can be connected. The practical quantum network could be brought into reality.In this paper, the quantum entanglement percolation protocol is proposed tooptimize the transmission of quantum entanglement in a network. The long-distanceentanglement establishment and transmission could be mapped into entanglementpercolation in a quantum network. While the threshold of percolation stands for the minimum amount of resource to achieve the transfer of quantum entanglement. Theclassical entanglement percolation (CEP) which doesn’t change the topology of thequantum network has limited potential to promote quantum entanglement transmission.By introducing a series of local quantum operation-“q-swap” into the classicalentanglement percolation, the quantum entanglement percolation (QEP) protocol isobtained. It is shown that the threshold of QEP is smaller than that of CEP and the reasonof this phenomenon is discussed.On the analysis of the "q-swap" operating principles, an operation called“target-swap” is introduce which is the expansion and improvement of “q-swap”operation. The "target-swap" quantum operation is studied if the structure of originalnetwork is not destroyed after the operation. It is found that the threshold of QEP is muchlower than that of CEP in the performance of long distance preparation and transmissionof quantum entanglement. That is, the QEP has obvious advantage over CEP. Thethreshold will be obviously influenced by different protocols of”swap”, different pairs ofentangled quantum states between nodes, and etc.