Programming of channels in generalized probabilistic theories

TL;DR

This paper extends the quantum no-programming theorem to generalized probabilistic theories, exploring how programming of dynamics relates to the structure of state spaces in GPTs.

Contribution

It generalizes the quantum no-programming theorem to GPTs and links reversible dynamics programming to quasi-classical structures.

Findings

Programming of reversible dynamics relates to quasi-classical structures.

A generalized no-programming theorem is derived for GPTs.

Investigation of irreversible dynamics programming in GPTs.

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 the 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 related closely 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.