Quantum Entanglement Percolation

TL;DR

This paper explores quantum entanglement percolation in quantum networks, demonstrating non-classical transition points that enable efficient entanglement distribution, including establishing perfect entanglement in a 1D chain with imperfect pairs.

Contribution

It introduces quantum networks with non-classical percolation transitions, offering new strategies for efficient quantum entanglement distribution over classical network models.

Findings

Quantum networks exhibit non-classical percolation transition points.

Perfect entanglement can be established in a 1D chain using imperfect pairs.

Quantum strategies outperform classical percolation in network connectivity.

Abstract

Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes evolution of network connectivity with respect to some network parameters. In this framework, the probability to establish perfect entanglement between two remote partners decays exponentially with the distance between them before the percolation transition point, which unambiguously defines percolation properties of any classical network or lattice. Here we introduce quantum networks created with local operations and classical communication, which exhibit non-classical percolation transition points leading to the striking communication advantages over those offered by the corresponding classical networks. We show, in particular, how to establish perfect entanglement between any two nodes in the simplest possible network -- the 1D chain -- using imperfect entangled pairs of qubits.