Concurrence Percolation in Quantum Networks

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