Concurrence Percolation in Quantum Networks

TL;DR

This paper introduces concurrence percolation theory (ConPT), a novel framework for understanding entanglement transmission in quantum networks that predicts lower thresholds for successful communication than classical models.

Contribution

The paper develops a new statistical theory, ConPT, that generalizes classical percolation to quantum entanglement, revealing a quantum advantage in network connectivity thresholds.

Findings

ConPT predicts lower entanglement transmission thresholds than classical percolation.

ConPT demonstrates universal critical behavior in various network geometries.

Quantum networks can achieve entanglement distribution more efficiently than classical predictions.

Abstract

Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical percolation assumes a necessary condition for successful entanglement transmission between any two infinitely distant nodes: they must be connected by at least a path of perfectly entangled states (singlets). Here, we relax this condition by explicitly showing that one can focus not on optimally converting singlets but on establishing concurrence -- a key measure of bipartite entanglement. We thereby introduce a new statistical theory, concurrence percolation theory (ConPT), remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. Inspired by resistance network analysis, we determine the path connectivity by series/parallel rules and approximate higher-order rules via star-mesh transforms. Interestingly, we find that the entanglement transmission threshold predicted by ConPT is lower than the known classical-percolation-based results and is readily achievable on any series-parallel networks such as the Bethe lattice. ConPT promotes our understanding of how well quantum communication can be further systematically improved versus classical statistical predictions under the limitation of QN locality -- a "quantum advantage" that is more general and efficient than expected. ConPT also shows a percolation-like universal critical behavior derived by finite-size analysis on the Bethe lattice and regular two-dimensional lattices, offering new perspectives for a theory of criticality in entanglement statistics.