Long Distance Entanglement Generation in 2D Networks

TL;DR

This paper introduces a global error correction method for 2D quantum networks that enables long-distance entanglement generation, comparing its effectiveness with entanglement percolation across different network configurations.

Contribution

It develops a novel global error correction scheme for 2D networks and explores its combination with percolation to enhance long-distance entanglement generation.

Findings

Global error correction can generate distance-independent entanglement with rank two states.

Combining error correction with percolation allows long-distance entanglement with rank three states.

Different schemes optimize for either perfect entanglement or broad connectivity, depending on network conditions.

Abstract

We consider 2D networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank two states. By using this method and combining it with the concept of percolation we also show that the generation of long distance entanglement is possible with rank three states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application on networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol can not generate a singlet between any two nodes. On the other hand, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.