Dynamics of the entanglement over noisy quantum networks

In this paper, the effect of homogeneous and non-homogeneous magnetic fields as an external noisy on the entanglement dynamics over partial entangled state quantum network is studied. The Dzyaloshiniskii-Moriya (DM) interaction is used to generate entangled network from partially entangled states in the presence of the spin-orbit coupling. The entanglement between any two nodes is quantified using Wootter concurrence. The effect of homogeneous and non-homogeneous magnetic field in presence and absence of the spin coupling on the entanglement between any two nodes of the network is investigated. The results show that the homogeneous magnetic field has no effect on the entanglement without the presence of the spin-orbit interaction. The non-homogeneous magnetic field has a strong impact on the entanglement either with or without spin-orbit couplings. For initially entangled channels, the upper bound does not exceed its initial value, whereas for the channels generated via indirect interaction, the entanglement reaches its maximum value.