  Device independent detections of quantum non-locality like Bell-CHSH
inequality are important methods to detect quantum non-locality because the
whole protocol can be implemented by uncertified local observables. However,
this detection is not sufficient for the justification of standard quantum
theory, because there are theoretically many types of beyond-quantum non-local
states in General Probabilistic Theories. One important class is Entanglement
Structures (ESs), which contain beyond-quantum non-local states even though
their local systems are completely equivalent to standard quantum systems. This
paper shows that any device independent detection cannot distinguish
beyond-quantum non-local states from standard quantum states. To overcome this
problem, this paper gives a device dependent detection based on local
observables to distinguish any beyond-quantum non-local state from all standard
quantum states. Especially, we give a way to detect any beyond-quantum
non-local state in two-qubit ESs by observing only spin observables on local
systems.
