  We work out a classification scheme for quantum modeling in Hilbert space of
any kind of composite entity violating Bell's inequalities and exhibiting
entanglement. Our theoretical framework includes situations with entangled
states and product measurements ('customary quantum situation'), and also
situations with both entangled states and entangled measurements ('nonlocal box
situation', 'nonlocal non-marginal box situation'). We show that entanglement
is structurally a joint property of states and measurements. Furthermore,
entangled measurements enable quantum modeling of situations that are usually
believed to be 'beyond quantum'. Our results are also extended from pure states
to quantum mixtures.
