One-shot and asymptotic classical capacity in general physical theories

Abstract: With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal rate of classical information transmitted by using a single channel under a constraint of a certain error probability, in general physical theories where states and measurements are operationally defined. Then we obtain the upper bound of one-shot classical capacity by generalizing the method given by Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)]. Also, we derive the lower bound of the capacity by showing the existence of a good code that can transmit classical information with a certain error probability. Applying the above two bounds, we prove the asymptotic equivalence between classical capacity and hypothesis testing relative entropy even in any general physical theory.