that are verified for every LHVT, but violated in quantum mechanics. Therefore, this demonstrates that there exist quantum states whose outcome probabilities are inconsistent with locality. Thus, the non-locality property of entangled states leading to a violation of Bell inequality does not satisfy the former rule (1). Very interestingly, after being a source of theoretical debate in the foundations of quantum mechanics and epistemology, more recently Bell non-locality has then emerged as a fundamental resource for quantum technologies [33], stimulating further studies on the topic and a consequent search for its deep understanding. Following this direction, a further form of quantum non-locality was then provided by [PERSON] [34], extending GHZ [35; 36] analysis. In this case one directly shows that there exist quantum states whose outcome possibilities are inconsistent with locality. In little more detail, by considering the GHZ state  
\[\cos(\alpha)|000\rangle+\sin(\alpha)|111\rangle \tag{3}\]  
he demonstrated that no LHVT can reproduce the quantum mechanics (QM) result for measurements \(X_{1}\otimes X_{2}\otimes X_{3}\), \(Y_{1}\otimes Y_{2}\otimes X_{3}\), \(Y_{1}\otimes X_{2}\otimes Y_{3}\) and \(X_{1}\otimes Y_{2}\otimes Y_{3}\). Interestingly, Mermin non-locality has also been recently included in categorical formulation of quantum mechanics [37]. Always in categorical formulation of quantum mechanics, it has been also demonstrated [21] that strong contextuality (exemplified by Mermin/GHZ non-locality) implies possibilistic non-locality (exemplified by [PERSON] non-locality [38]) that implies probabilistic non-locality (exemplified by [PERSON]'s inequalities). It is interesting at this point to put in evidence that, aside important contributions on generalizations to non-deterministic hidden variable (HV) theories, [PERSON] coined also the inspired and elegant definition [39]: \"the non-locality property of quantum mechanics is the logical need for information about a choice of experiment freely made in one region to be present in a second region that is space-like separated from the first\". The hidden variable \(x\) is usually considered as a \"property\" that the two measured physical systems posses because of their generation from a certain common source (for example for an entangled photon pairs emerging from a spontaneous parametric down-conversion crystal). If the two measurements are space-like separated events their outcomes exhibit a local dependence on the experimental settings and on \(x\) itself. Given these conditions, following Ref. [30] it is possible to demonstrate that these models fail when an experiment is designed to implement two distinct and independent sources generating entangled pairs, therefore entailing two independent sets \(x_{1},x_{2}\) of HVs, and the visibility overcomes the threshold of 50% in entanglement swapping [40] (it is worth to notice that in the case of experiments verifying Bell inequalities the required visibility is 71%). More in general, \(x\) can be explained as the state describing the two systems [22], or even the whole universe. In this case, referring to Equation (1) the requirements on \(A\), \(B\) measurements imply that the dependence does not rely on \(x\) only, i.e., \(x\) can be a non-local beable with the only condition that the local inputs \(A,B\) together with the global state \(x\) determine the outcome probabilities (note that Ref. [22] uses the word \"propensities\" instead of probabilities for emphasizing that probability cannot be considered in Kolgomorov sense, since in this case it can always be interpreted as epistemic). Moreover, in Ref. [22] it is argued that whether a deterministic model is considered, or epistemic probabilities are taken into account, problems arise related to independence of outcomes from reference frame. Bell non-locality (1) makes reference to hidden variables \(x\) (\"ontological\" version), and as stated in ref.