Trade-off Relations in Genuine Four-qubit Nonlocality Systems

We investigate trade-off relations governing genuine four-qubit nonlocality in multipartite quantum systems. By analyzing the reduced four-qubit density operators obtained from five-qubit generalized GHZ and MS states, we establish nontrivial constraints on the expectation values of the SeevinckSvetlichny operators associated with these subsystems. In particular, we demonstrate that genuine four-qubit nonlocal correlations across different four-qubit reductions are not mutually independent. For both classes of five-qubit states considered, we show that the sum of the maximal squared expectation values of the Seevinck-Svetlichny operators over all four-qubit reductions is subject to a state-dependent upper bound. Furthermore, this collective bound is shown to be tighter than the bounds obtained by independently imposing the maximal allowed expectation value of the Svetlichny operator on each four-qubit subsystem. These results reveal a monogamy-like trade-off structure for genuine four-qubit nonlocal correlations and provide tighter constraints on their simultaneous manifestation in multipartite quantum systems.