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The principle of signal locality (violated in non-equilibrium Valentini post-quantum mechanics) demands:

"Physical principles impose limits on the correlations observed by distant parties. It is known, for instance, that the principle of no-signalling—that is, the fact that the correlations cannot lead to any sort of instantaneous communication—implies no-cloning [1] and no- broadcasting [2] theorems, and the possibility of secure key distribution [3]. Moving to the quantum domain, the main goal of quantum information theory is precisely to understand how quantum properties may be used for in- formation processing. It is then important to understand how the quantum formalism constrains the correlations amongst distant parties. ... There is an ongoing effort to understandthe gap between quantum and nonsignalling correlations. As stated above, there exist correlations which, despite being compatible with the no-signalling principle, cannot be attained by local measurements on a quantum state. The natural question is then to study why these supra-quantum correlations do not seem to be observed in nature... In this work, we introduce a unified mathematical for- malism for nonsignalling and quantum correlations in terms of local quantum observables. We expect this formalism to be useful when tackling all such questions. It may be easier using our construction to study how new constraints may be added to the nonsignalling principle in order to derive the quantum correlations. ... Our results imply that this decomposition is not possible for all N-party entanglement witnesses. It would be interesting to better understand why the theorem fails in the multi-partite scenario and identify additional requirements able to close the gap."

Phys. Rev. Lett. 104, 140404 (2010) [4 pages]