Programming of channels in generalized probabilistic theories

Abstract

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