  In a quantum communication network, links represent entanglement between
qubits located at different nodes. Even if two nodes are not directly linked by
shared entanglement, communication channels can be established between them via
quantum routing protocols. However, in contrast to classical communication
networks, each communication event removes all participating links along the
communication path, disrupting the quantum network. Here, we propose a simple
model, where randomly selected pairs of nodes communicate through shortest
paths. Each time such a path is used, all participating links are eliminated,
leading to a correlated percolation process that we call ``path percolation.''
We study path percolation both numerically and analytically and present the
phase diagram of the steady states as a function of the rate at which new links
are being added to the quantum communication network. As a key result, the
steady state is found to be independent from the initial network topology when
new link are added randomly between disconnected components. We close by
discussing extensions of path percolation and their potential applications.
