Multipartite standard nonlocality sharing by m-sided independent sequential observers

The sharing of quantum nonlocality has been the subject of much recent research for two-qubit and three-qubit entangled systems. In this paper, we discuss nonlocality sharing with unsharp measurement based on Mermin–Ardehali–Belinskii–Klyshko (MABK) inequality for the N-qubit generalized Greenberger–Horne–Zeilinger (GHZ) system. In the one-sided sequential measurements scenario, we determine a state range associated with k within which \( k+1 \) independent observers can share the standard N-partite nonlocality with the other \((N-1)\) sides, as well as a state range where arbitrarily many independent observers can do the same. Similarly, as to the m-sided sequential measurements scenario, we also identify a state range influenced by k within which \( k+1 \) independent observers in each of m sides can share the standard N-partite nonlocality with the other \((N-m)\) sides, and a state range where arbitrarily many independent observers can do so. Crucially, all of our nonlocality sharing findings result from a measurement strategy in which every sequential observer employs unequal sharpness measurements. As a special case, for the three-qubit maximally entangled GHZ state, we demonstrate that an unbounded number of observers can share the nonlocality in the one-sided sequential measurements scenario. This outcome further underscores the importance of unequal sharpness measurements in recycling qubits for generating quantum nonlocality.