## 2 Various Questions on Quantum Non-Locality
[119] describes and experimentally tests a new criterion founded on entropy functions, violated by more states. In [120] it was investigated whether the phenomenon of EPR steering can also be generalized beyond quantum theory demonstrating that, whilst post-quantum steering does not exist in the bipartite case, it is present in the case of three observers and it is fundamentally different from postquantum non-locality. An interesting discussion on the connections between non-locality and complementarity can be found in [121], in which the key point focuses on the possibility to attribute different operational meanings to the concept of joint measurability of two observables (A,B): (i) A and B values can be obtained by the measurement of a third observable C (in the sense that the probability distribution of A and B outcomes are included as marginals in the distribution of C results); (ii) when the sequence ABA is measured, the two measurements of the same observable A return identical outcomes; (iii) if the measurement sequence AB is considered, the same probability distribution over B outcomes is obtained as a direct B measurement. In the context of quantum mechanics there is a total equivalence among all these statements, nevertheless Ref. [121] describes that for any no-signalling theory not showing complementarity (as specified at item (iii) it is allowed a local realistic description, but this is not valid with respect to properties i and ii (the demonstration took advantage of non-local box correlations models). In addition, it is worth to mention the research [75] that analyzes the comparison among the structures of entanglement correlations with respect to the non-local ones, putting in evidence significant differences. The concept of \"unit of non-locality\" is speculated as a possible explanation for a PR-box, and proven that this is not applicable to describe correlations when cluster states are considered. In [122; 123; 124; 125] an investigation on other aspects of PR-box is extended. Moreover, the paper [126] analyzes the possibility to build a covariant deterministic non-local HV extension of quantum theory, and demonstrates how it is possible to reduce any covariant non-local variable to Bell local variable whose existence is known to be incompatible with well-tested quantum predictions. Another fundamental problem considered in Ref. [127] is related to whether the non-locality of a quantum state can be superactivated, in other words if a state \(\rho\otimes\rho\) can be considered non-local if \(\rho\) is local. This aspect, that refers to a sort of additivity property of non-locality, has been analyzed by considering unbounded [128] Bell inequalities, returning the conclusion that if a number of local entangled states are combined by direct product, it is possible to get a non-local global state, falsifying in this way the forementioned additivity. In conclusion, as an extension of this study it was considered the possibility for any kind of local entangled state to generate non-locality superactivation, and demonstrated [129] that all quantum states useful for teleportation represent non-local resources.