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Physical theories with local structure similar to quantum theory can allow beyond-quantum global states that are in agreement with unentangled Gleason's theorem. In a standard Bell experiment any such bipartite state produces correlations that are always quantum simulable. In this limited classical-input-classical-output Bell scenario, we show that there exist bipartite beyond-quantum states that produce correlations all of which are in-fact classically simulable. However, if the type of Bell scenario is generalized to consider quantum states as inputs, we then show that any such bipartite beyond-quantum state yields beyond-quantum input-output correlations. We also analyze the implication of this quantum input scenario while studying generic multipartite correlations obtained from local quantum theory but potentially allowing different global structure. Our study suggests the requirement of type sensitive information principles for isolating the quantum correlations from the beyond-quantum ones.Introduction.-Correlations among distant events established through the violation of Bell type inequalities confirm nonlocal behavior of the physical world [1][2][3][4]. Nonseparable multipartite quantum states yielding such correlations, in Schrödinger's words, are "...the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought" [5]. The advent of quantum information science identifies the power of such nonlocal correlations in numerous device independent protocols -cryptographic key distribution [6], randomness certification [7] and amplification [8], dimension witness [9] are few canonical examples. Cirel'son's result [10], however, establishes that the nonlocal strength of quantum correlations is limited compared to the general no-signaling (NS) ones [11] as depicted in the celebrated Clauser-Horne-Shimony-Holt (CHSH) inequality violation [12].

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