Entanglement percolation in random quantum networks

TL;DR

This paper investigates entanglement percolation in quantum networks with randomly distributed initial entanglement, revealing how heterogeneity affects protocol efficiency and suggesting new strategies for realistic networks.

Contribution

It generalizes entanglement percolation protocols to heterogeneous networks and compares classical and quantum strategies under randomness.

Findings

Classical entanglement percolation depends only on average initial entanglement.

Quantum entanglement percolation degrades as the distribution of initial entanglement widens.

Random CEP may outperform quantum protocols in highly heterogeneous networks.

Abstract

Entanglement percolation aims at generating maximal entanglement between any two nodes of a quantum network by utilizing strategies based solely on local operations and classical communication between the nodes. As it happens in classical percolation theory, the topology of the network is crucial, but also the entanglement shared between the nodes of the network. In a network of identically partially entangled states, the network topology determines the minimum entanglement needed for percolation. In this work, we generalize the protocol to scenarios where the initial entanglement shared between any two nodes of the network is not the same but has some randomness. In such cases, we find that for classical entanglement percolation, only the average initial entanglement is relevant. In contrast, the quantum entanglement percolation protocol (within the q-swap framework) degrades under these more realistic conditions as the width of the distribution increases, suggesting that Random CEP may become the optimal LOCC strategy in sufficiently heterogeneous quantum networks.