Quantum process discrimination with restricted strategies.

The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when discrimination strategies are restricted to a given subset of all strategies allowed by quantum mechanics. In this paper, we show that the task of finding the maximum success probability for discriminating any quantum processes with any restricted strategy can always be formulated as a convex optimization problem whose Lagrange dual problem exhibits zero duality gap. We also derive a necessary and sufficient condition for an optimal restricted strategy to be optimal within the set of all strategies. As an application of this result, it is shown that adaptive strategies are not necessary for optimal discrimination if a problem has a certain symmetry. Moreover, we show that the optimal performance of each restricted process discrimination problem can be written in terms of a certain robustness measure. This finding has the potential to provide a deeper insight into the discrimination performance of various restricted strategies.