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Crucial problems of the quantum Internet are the derivation of stabilityproperties of quantum repeaters and theory of entanglement rate maximization inan entangled network structure. The stability property of a quantum repeaterentails that all incoming density matrices can be swapped with a target densitymatrix. The strong stability of a quantum repeater implies stable entanglementswapping with the boundness of stored density matrices in the quantum memoryand the boundness of delays. Here, a theoretical framework of noise-scaledstability analysis and entanglement rate maximization is conceived for thequantum Internet. We define the term of entanglement swapping set that modelsthe status of quantum memory of a quantum repeater with the stored densitymatrices. We determine the optimal entanglement swapping method that maximizesthe entanglement rate of the quantum repeaters at the different entanglementswapping sets as function of the noise of the local memory and localoperations. We prove the stability properties for non-complete entanglementswapping sets, complete entanglement swapping sets and perfect entanglementswapping sets. We prove the entanglement rates for the different entanglementswapping sets and noise levels. The results can be applied to the experimentalquantum Internet.

Theory of Noise-Scaled Stability Bounds and Entanglement Rate Maximization in the Quantum Internet