  Building large-scale quantum communication networks has its unique
challenges. Here, we demonstrate that a network-wide synergistic usage of
quantum memories distributed in a quantum communication network offers a
fundamental advantage. We first map the problem of quantum communication with
local usage of memories into a classical continuum percolation model. Then, we
show that this mapping can be improved through a cooperation of entanglement
distillation and relay protocols via remote access to distributed memories.
This improved mapping, which we term $\alpha$-percolation, can be formulated in
terms of graph-merging rules, analogous to the decimation rules of the
renormalization group treatment of disordered quantum magnets. These rules can
be performed in any order, yielding the same optimal result, which is
characterized by the emergence of a ``positive feedback'' mechanism and the
formation of spatially disconnected ``hopping'' communication components --
both marking significant improvements in quantum network connectivity.
