Large parts are generically entangled across all cuts

Abstract Generic bipartite pure states of sufficiently large dimensions are overwhelmingly likely to be highly entangled. However, unlike the bipartite setting, the entanglement of generic multipartite pure states, and specifically their multipartite marginals , is far less understood. Here, we show that sufficiently large marginals of generic multipartite pure states, accounting for approximately half or more of the subsystems, are entangled across all bipartitions. These pure states are thus robust to losses in entanglement distribution. Moreover, even without assuming that the global state is pure, a small number of overlapping entangled marginals of generic pure states—as we show in this work—must induce entanglement in other marginals when some mild dimension constraints are satisfied, i.e. entanglement transitivity is a generic feature of various many-body pure states. Numerically, we further observe that the genericity of (1) entangled marginals, (2) unique global compatibility, and (3) entanglement transitivity may also hold beyond the analytically established dimension constraints. We also discuss potential applications of these features of generic pure states in quantum information processing.