Concurrence Percolation in Quantum Networks

In this talk, I will explain how entanglement distribution on quantum networks (QN) is traditionally understood by mapping to classical percolation theory, which gives rise to a nontrivial threshold---in terms of the entanglement per link---for possibly transmitting entanglement between two arbitrarily distant nodes in QN. However, such a traditional comprehension is not complete. Indeed, a lower entanglement transmission threshold than what classical percolation predicts exists, as demonstrated on special network topology, that reveals a large-scale "quantum advantage." Naturally, we ask: Is such a "quantum advantage" general regardless of topology? I will address this question by introducing a new statistical theory, concurrence percolation theory (ConPT), that is remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. ConPT predicts a lower threshold than classical percolation for any network topology, showing that the existence of a large-scale "quantum advantage" is indeed general on any QN. [For more details see: Meng, X., Gao, J. & Havlin, S. Concurrence Percolation in Quantum Networks (https://arxiv.org/abs/2103.13985).]