  Recently, the resource theory of asymmetric distinguishability for quantum
strategies was introduced by [Wang et al., Phys. Rev. Research 1, 033169
(2019)]. The fundamental objects in the resource theory are pairs of quantum
strategies, which are generalizations of quantum channels that provide a
framework to describe an arbitrary quantum interaction. In the present paper,
we provide semi-definite program characterizations of the one-shot operational
quantities in this resource theory. We then apply these semi-definite programs
to study the advantage conferred by adaptive strategies in discrimination and
distinguishability distillation of generalized amplitude damping channels. We
find that there are significant gaps between what can be accomplished with an
adaptive strategy versus a non-adaptive strategy.
