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We propose a measurement-based entanglement propagation strategy for networksin which all nodes except two are initially occupied by a suitably chosensingle-qubit system and the two nodes share a bipartite noisy entangled state.The connections between the sites are established using unsharp two-qubitmeasurements. When only a single node performs measurements, we refer to it asa unidirectional protocol while when both parts of the initial entangled statesperform measurements, we call it a bidirectional scheme. When the measurementoutcome is post-selected, we demonstrate that in the presence of a localamplitude damping channel acting on a single site, entanglement shareability,as measured by the monogamy score, of the resulting state after measurement canbe higher for all values of the strength of the noise than that of the scenariowithout noise. We observe that irrespective of the channel, there exists arange of unsharpness parameter where a higher monogamy score may be obtainedstarting from the initial nonmaximally entangled states than from the initialmaximally entangled state. We report that the effect of noise on the averagemonogamy score entered from the resource state may be reduced faster with theunidirectional protocol than with the bidirectional one.

Duality between imperfect resources and measurements for propagating entanglement in networks