Quantum entanglement percolation under a realistic restriction

The problem of establishing Bell and Greenberger-Horne-Zeilinger states between faraway places or distant nodes of a circuit is a difficult and an extremely important one, and a strategy which addresses it is entanglement percolation. We provide a method for attaining the end through a quantum measurement strategy involving three-, two-, and single-qubit measurements on a single-layer honeycomb lattice of partially entangled pure bipartite entangled states. We then move over to a double-layered lattice, and introduce entanglement percolation on that lattice under a realistic restriction on local quantum operations and classical communication allowed on the nodes of the lattice. When applied to a single-layered honeycomb lattice, our strategy would call for less noise effects in an actual realization than when the same phenomenon is attained via existing methods. Moreover, for the double-layered honeycomb lattice, we report advantage of quantum entanglement percolation over classical entanglement percolation under the realistic restriction.