A quantum network is a network of entangled states, which can be used to transmit quantum information. Nonmaximally entangled states are not really effective in establishing quantum communication across vast distances. Creating and maintaining a maximally entangled state over which quantum information can be transferred more effectively is difficult in experiments, as nonmaximally entangled states are typically produced there. Therefore, we usually construct a network of nonmaximally entangled states and use the underlying network structure to establish maximal entanglement between distant nodes. Various protocols leveraging interesting aspects of quantum and statistical physics are designed to achieve long-range maximally entangled states. Here, we consider two-dimensional lattices as quantum networks where edges represent nonmaximally entangled pure states. We introduce a general protocol based on bond percolation -- general concurrence percolation (GCP) -- to create a network of maximally entangled states. The associated network obtained through GCP ought to enable the achievement of long-range quantum communication. Our observations indicate that, similar to other existing protocols, GCP falls within the percolation universality class, as determined through finite-size scaling analysis performed on two-dimensional lattices. We find that the associated percolation threshold value is smaller than that of the existing protocols. We introduce and analytically solve a minimal model that renders insight into the origin of the fundamentally lower percolation threshold achieved by GCP.

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