  We study entanglement activation in a generalized entanglement swapping
process involving two Bell pairs and generalized measurements. The conventional
understanding posits entangled measurements as both necessary and sufficient
for establishing entanglement between distant parties. In this study, we
reassess the role of measurement operators in entanglement generation within a
generalized entanglement swapping process. We focus on maximally entangled
two-qubit initial states and generalized measurements, investigating the
necessity and sufficiency conditions for entangled measurement operators. By
utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4)
shared between Bob and Charlie, we demonstrate that while entangled
measurements are sufficient, they are not indispensable for establishing
entanglement between spatially separated observers. Through a sequential
approach, if Bob performs an initial measurement which is not able to establish
entanglement then followed by another measurement after post-processing the
first measurement it is possible to establish entanglement. We identify
specific criteria for different measurement operators that enable the potential
for performing a second measurement to establish entanglement. Our findings
highlight the feasibility of generating entanglement between distant parties
through a combination of measurements, shedding light on entanglement
distribution in quantum networks. Additionally, we showcase through
illustrative examples how successive measurements enhance entanglement compared
to single measurements, underscoring the practical benefits of our approach in
enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit
states to higher-dimensional maximally entangled states, emphasizing its
versatility and applicability.
