Entanglement Distribution in Pure-State Quantum Networks

TL;DR

This paper explores optimal strategies for distributing entanglement in pure-state quantum networks, revealing surprising measurement protocols and demonstrating the possibility of establishing perfect entanglement over large distances.

Contribution

It introduces new optimal measurement protocols for entanglement distribution in small and large quantum networks, challenging previous assumptions about Bell measurements.

Findings

Bell measurements are not always optimal for entanglement distribution.

Perfect entanglement can be achieved over large networks with high initial entanglement.

Hierarchical and 2D networks can establish long-distance entanglement in finite steps.

Abstract

We investigate entanglement distribution in pure-state quantum networks. We consider the case when non-maximally entangled two-qubit pure states are shared by neighboring nodes of the network. For a given pair of nodes, we investigate how to generate the maximal entanglement between them by performing local measurements, assisted by classical communication, on the other nodes. We find optimal measurement protocols for both small and large 1D networks. Quite surprisingly, we prove that Bell measurements are not always the optimal ones to perform in such networks. We generalize then the results to simple small 2D networks, finding again counter-intuitive optimal measurement strategies. Finally, we consider large networks with hierarchical lattice geometries and 2D networks. We prove that perfect entanglement can be established on large distances with probability one in a finite number of steps, provided the initial entanglement shared by neighboring nodes is large enough. We discuss also various protocols of entanglement distribution in 2D networks employing classical and quantum percolation strategies.