  We study a broad class of quantum process discrimination problems that can
handle many optimization strategies such as the Bayes, Neyman-Pearson, and
unambiguous strategies, where each process can consist of multiple time steps
and can have an internal memory. Given a collection of candidate processes, our
task is to find a discrimination strategy, which may be adaptive and/or
entanglement-assisted, that maximizes a given objective function subject to
given constraints. Our problem can be formulated as a convex problem. Its
Lagrange dual problem with no duality gap and necessary and sufficient
conditions for an optimal solution are derived. We also show that if a problem
has a certain symmetry and at least one optimal solution exists, then there
also exists an optimal solution with the same type of symmetry. A minimax
strategy for a process discrimination problem is also discussed. As
applications of our results, we provide some problems in which an adaptive
strategy is not necessary for optimal discrimination. We also present an
example of single-shot channel discrimination for which an analytical solution
can be obtained.
