Percolation transition control in quantum networks

Antonio Acín, J. I. Cirac, Maciej Lewenstein

Shashaank Khanna, Ujjwal Sen, Sarika Jalan

Gaogao Dong, Yili Shen, Xinqi Hu +1 more

The evolution of connectivity in quantum networks under decoherence and link degradation is a central problem in quantum information, calling for further understanding of the nature of its transition during structural network degradation. By diluting each link with probability 1−f, we focus on connectivity strength transitions in diluted hierarchical scale-free quantum networks, the (u,v) flowers, which are analytically tractable through two adjustable path-length parameters, u≤v. Incorporating quantum concurrence percolation and comparing it with classical percolation, we analyze the transitions of critical thresholds for various values of f and v from analytical, numerical, and simulation perspectives. The results demonstrate that quantum percolation exhibits consistently lower critical thresholds than classical percolation, even under various topologies and dilution levels. Our work implies that quantum multipath entanglement provides an intrinsic compensatory mechanism against structural degradation and that the hierarchical scale-free topology contributes to the failure resistance and robustness of quantum networks with multipath coupling.

Michael Siomau

A sudden change in size, number, or extent is rare, yet highly desired effect in theoretical models. The abrupt emergence of large-scale connectivity in a percolating network near the transition point gained the name explosive percolation. Classical network science lacks a simple recipe for explosiveness. Quantum networks governed by the laws of quantum mechanics intrinsically possess such an explosive component due to quantum superposition and measurements, which may be employed to achieve macroscopic explosiveness. Any percolating quantum network may exhibit explosive properties due to different state preparation and observation strategies near the transition point.

Liang Cao, M. Jeng, Jennifer M. Schwarz

Siomau, M.

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 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 imperfectly entangled pairs of qubits.