Abstract
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.