  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.
