Programming of channels in generalized probabilistic theories

For a given target system and apparatus described by quantum theory, the so-called no-programming theorem indicates that family of states called programs in with fixed unitary operation on total distinct dynamics to only if initial are orthogonal each other. The current study aims at revealing whether similar behavior can be observed generalized probabilistic theories (GPTs). Generalizing programming scheme GPTs, we derive theorem. We, furthermore, demonstrate reversible is closely related curious structure named quasi-classical state space. Programming irreversible dynamics, i.e., channels, GPTs also investigated.