Limited path entanglement percolation in quantum complex networks
arXiv:1011.5630 · doi:10.1103/PhysRevA.83.032319
Abstract
We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted through them. For pure quantum state links, quantum networks exhibit a remarkable feature absent in classical networks: it is possible to effectively rewire the network by performing local operations on the nodes. We propose a family of such quantum operations that decrease the entanglement percolation threshold of the network and increase the size of the giant connected component. We provide analytic results for complex networks with arbitrary (uncorrelated) degree distribution. These results are in good agreement with numerical simulations, which also show enhancement in correlated and real world networks. The proposed quantum preprocessing strategies are not robust in the presence of noise. However, even when the links consist of (noisy) mixed state links, one can send quantum information through a connecting path with a fidelity that decreases with the path length. In this noisy scenario, complex networks offer a clear advantage over regular lattices, namely the fact that two arbitrary nodes can be connected through a relatively small number of steps, known as the small world effect. We calculate the probability that two arbitrary nodes in the network can successfully communicate with a fidelity above a given threshold. This amounts to working out the classical problem of percolation with limited path length. We find that this probability can be significant even for paths limited to few connections, and that the results for standard (unlimited) percolation are soon recovered if the path length exceeds by a finite amount the average path length, which in complex networks generally scales logarithmically with the size of the network.
15 pages, 18 figures
References in corpus (30)
- Error and attack tolerance of complex networks
- The Quantum Internet
- The diameter of the world wide web
- Random graphs with arbitrary degree distributions and their applications
- Network robustness and fragility: Percolation on random graphs
- Resilience of the Internet to random breakdowns
- Critical phenomena in complex networks
- Breakdown of the Internet under intentional attack
- Quantum repeaters based on entanglement purification
- Absence of epidemic threshold in scale-free networks with connectivity correlations
- Random graphs with clustering
- Entanglement of pure states for a single copy
- Entanglement Percolation in Quantum Networks
- Exact solution of site and bond percolation on small-world networks
- Optimal teleportation with a mixed state of two qubits
- Percolation on correlated networks
- Quantum complex networks
- Entanglement Distribution in Pure-State Quantum Networks
- Entanglement percolation in quantum complex networks
- Metric structure of random networks
- Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality
- Fractal Boundaries of Complex Networks
- Correlations in connected random graphs
- Limited path percolation in complex networks
- Multipartite entanglement percolation
- Fidelity threshold for long-range entanglement in quantum networks
- Entanglement Percolation with Bipartite Mixed States
- Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations
- Singlet Generation in Mixed State Quantum Networks
- Long Distance Entanglement Generation in 2D Networks
Cited by in corpus (16)
- Percolation on complex networks: Theory and application
- Google in a Quantum Network
- Distribution of entanglement in large-scale quantum networks
- Complex Quantum Networks: a Topical Review
- Concurrence Percolation in Quantum Networks
- Growth of graph states in quantum networks
- Thermodynamic formalism for dissipative quantum walks
- Bipartite quantum states and random complex networks
- Performance metrics for the continuous distribution of entanglement in multi-user quantum networks
- Information sharing in Quantum Complex Networks
- Unitary Entanglement Construction in Hierarchical Networks
- Quantum Entanglement Percolation
- Entanglement percolation in random quantum networks
- The role of local and global geometry in quantum entanglement percolation
- Renormalization and small-world model of fractal quantum repeater networks
- Quantum Google Algorithm: Construction and Application to Complex Networks