Linear response of tripartite entanglement to infinitesimal noise

• We study a set of W-type noise and its linear effect on symmetric pure states.
• Its effect on two-qubit entanglement depends only on the initial concurrence.
• A lower bound of the effect on 3-tangle is found in terms of initial entanglements.
• We obtain the time of three-tangle sudden death for two families of typical states.
• These reveal that the bipartite entanglement speeds up the decay of the tripartite one.

Recent experimental progress in prolonging the coherence time of a quantum system prompts us to explore the behavior of quantum entanglement at the beginning of the decoherence process. The response of the entanglement under an infinitesimal noise can serve as a signature of the robustness of entangled states. A crucial problem of this topic in multipartite systems is to compute the degree of entanglement in a mixed state. We find a family of global noise in three-qubit systems, which is composed of four W states. Under its influence, the linear response of the tripartite entanglement of a symmetrical three-qubit pure state is studied. A lower bound of the linear response is found to depend completely on the initial tripartite and bipartite entanglement. This result shows that the decay of tripartite entanglement is hastened by the bipartite one.