Sharing Genuine Entanglement of Generalized Tripartite States by Multiple Sequential Observers

Genuine entanglement serves as a valuable resource for multipartite quantum information processing. Recently, the ability to share the genuine entanglement among a long sequence of independent observers has gained considerable attention, especially when the state preparation faces significant limitations. Firstly, this paper focuses on investigating the sharing ability of genuine tripartite entanglement under unilateral sequential measurements. We propose a measurement strategy for generalized tripartite Greenberger-Horne-Zeilinger (GHZ) states to enable arbitrarily long sequence of independent observers to detect the genuine entanglement using entanglement witnesses. Moreover, when the sharpness parameters of each sequential observer’s measurement settings are equal, we give the correlation between the controllable angle of generalized GHZ state and the maximum number of sequential observers capable of detecting genuine entanglement. In particular, we identify the controllable angle range within which the same number of such observers can be achieved for generalized GHZ states as with the maximally entangled GHZ state. We also determine the controllable angle range for generalized tripartite \(\varvec{W}\) $\mathit{W}$ states, where the number of sequential observers can be same as that with maximally entangled \(\varvec{W}\) $\mathit{W}$ state. Furthermore, we design a measurement strategy for the trilateral sequential scenario, demonstrating that the genuine tripartite entanglement of any generalized GHZ state can be shared by arbitrarily many groups of observers.