  Modern quantum engineering techniques enabled successful foundational tests
of quantum mechanics. Yet, the universal validity of quantum postulates is an
open question. Here we propose a new theoretical framework of Q-data tests,
which recognises the established validity of quantum theory, but allows for
more general -- 'post-quantum' -- scenarios in certain physical regimes. It can
accommodate a large class of models with modified quantum wave dynamics,
correlations beyond entanglement or general probabilistic postulates. We
discuss its experimental implementation suited to probe the nature of strong
nuclear interactions. In contrast to the present accelerator experiments, it
shifts the focus from high-luminosity beam physics to individual particle
coherent control.
