Sequential sharing of entanglement via probabilistic projective measurements

Recently, Sasmal et al. [Phys. Rev. Lett. 133, 170201 (2024)] introduced probabilistic projective measurements (PPMs) for sequential sharing of nonlocality. Here we develop a general framework for sequentially witnessing quantum correlations, including bipartite and genuine multipartite entanglement, via PPMs. We show that a class of positive-operator-valued measures admits a unified PPM realization and present an explicit formula linking the initial state, intermediate channels, and witness operators, providing both computational efficiency and structural insight. Using this framework, we demonstrate unbounded sequential entanglement sharing for pure and certain mixed states, as well as detection of genuine multipartite entanglement in Greenberger-Horne-Zeilinger-type states. Our results highlight the nontrivial role of PPMs in sequential entanglement witnessing and address generalized multipartite sharing, as discussed in a recent review article [Phys. Rep. 1098, 1 (2025)].