A well known fact is that there is a finite orthomodular lattice with an
order determining set of states which is not representable in the standard
quantum logic, the lattice L(H) of all closed subspaces of a
separable complex Hilbert space.
We show that a generalized effect algebra is representable in the operator
generalized effect algebra GD(H) of effects of a
complex Hilbert space H iff it has an order determining set of
generalized states.
This extends the corresponding results for effect algebras of Rie\v{c}anov\'a
and Zajac. Further, any operator generalized effect algebra GD(H) possesses an order determining set of generalized states