  The state space structure for a composite quantum system is postulated among
several mathematically consistent possibilities that are compatible with local
quantum description. For instance, unentangled Gleason's theorem allows a state
space that includes density operators as a proper subset among all possible
composite states. However, bipartite correlations obtained in Bell type
experiments from this broader state space are in-fact quantum simulable, and
hence such spacelike correlations are no good to make distinction among
different compositions. In this work we analyze communication utilities of
these different composite models and show that they can lead to distinct
utilities in a simple communication game involving two players. Our analysis,
thus, establishes that beyond quantum composite structure can lead to beyond
quantum correlations in timelike scenario and hence welcomes new principles to
isolate the quantum correlations from the beyond quantum ones. We also prove a
no-go that the classical information carrying capacity of different such
compositions cannot be more than the corresponding quantum composite systems.
