Description:

Quantum networks describe communication networks that are based on quantum entanglement. Quantum networks differ from classical networks since the topology of a quantum network can be altered through local operations and classical communication. This makes it difficult to determine the percolation threshold of a quantum network. This problem can be solved by concurrence percolation theory by determining the minimum entanglement threshold at which a phase transition occurs in the total concurrence of the network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. We develop a set of mathematical tools for approximating the concurrence percolation threshold for large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 200^2 nodes and complex networks of up to 10^4 nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved.

Omar Malik, Renssalear Polytechnic Institute

Host: Istvan Kovacs