A counter-intuitive low entanglement percolation threshold in mixed-state quantum networks

Understanding entanglement percolation across quantum networks (QNs) has been a persistent challenge. Concurrence percolation theory (ConPT) provides a statistical-physics framework for this, drawing parallels between entanglement measure (concurrence) and classical percolation measure (probability). However, ConPT’s reach has been confined to idealized, pure-state entanglement resources, overlooking realistic mixed states “contaminated” by stochastic noise. This work extends into this realistic domain, introducing a mixed-state ConPT that reveals a percolation threshold lower than the pure-state counterpart. This paradoxical finding seemingly suggests that stochastic contamination is less detrimental than purity-preserving unitary noise, a notion that challenges conventional belief. We resolve this finding by highlighting an operational detail: implementing mixed-state ConPT effectively requires quantum memory to buffer the probabilistic nature of mixed-state protocols. We find evidence that without quantum memory, mixed-state ConPT consistently underperforms pure-state ConPT. This reinforces our understanding that stochastic noise poses a more significant impediment, a critical consideration for QN design. Understanding how entanglement spreads across realistic quantum networks, which are inevitably affected by environmental noise, is a key challenge. The authors show that a noisy network only appears to outperform an ideal one if it is supported by quantum memory, confirming that noise remains a critical barrier.