  We consider the problem of discriminating finite-dimensional quantum
processes, also called quantum supermaps, that can consist of multiple time
steps. Obtaining the ultimate performance for discriminating quantum processes
is of fundamental importance, but is challenging mainly due to the necessity of
considering all discrimination strategies allowed by quantum mechanics,
including entanglement-assisted strategies and adaptive strategies. In the case
in which the processes to be discriminated have internal memories, the ultimate
performance would generally be more difficult to analyze. In this paper, we
present a simple upper bound on the ultimate success probability for
discriminating arbitrary quantum processes. In the special case of multi-shot
channel discrimination, it can be shown that the ultimate success probability
increases by at most a constant factor determined by the given channels if the
number of channel evaluations increases by one. We also present a lower bound
based on Bayesian updating, which has a low computational cost. Our numerical
experiments demonstrate that the proposed bounds are reasonably tight. The
proposed bounds do not explicitly depend on any quantum phenomena, and can be
readily extended to a general operational probabilistic theory.
