  Quantum state exclusion is an operational task that has significance in
studying foundational questions related to interpreting quantum theory. In such
a task, one is given a system whose state is randomly selected from a finite
set, and the goal is to identify a state from the set that is not the true
state of the system. An error, i.e., an unsuccessful exclusion, occurs if and
only if the state identified is the true state. In this paper, we study the
optimal error probability of quantum state exclusion and its error exponent --
the rate at which the error probability decays asymptotically -- from an
information-theoretic perspective. Our main finding is a single-letter upper
bound on the error exponent of state exclusion given by the multivariate
log-Euclidean Chernoff divergence, and we prove that this improves upon the
best previously known upper bound. We also extend our analysis to the more
complicated task of quantum channel exclusion, and we establish a single-letter
and efficiently computable upper bound on its error exponent, even assuming the
use of adaptive strategies. We derive both upper bounds, for state and channel
exclusion, based on one-shot analysis and formulate them as a type of
multivariate divergence measure called a barycentric Chernoff divergence.
Moreover, our result on channel exclusion has implications in two important
special cases. First, for the special case of two hypotheses, our upper bound
provides the first known efficiently computable upper bound on the error
exponent of symmetric binary channel discrimination. Second, for the special
case of classical channels, we show that our upper bound is achievable by a
nonadaptive strategy, thus solving the exact error exponent of classical
channel exclusion and generalising a similar result on symmetric binary
classical channel discrimination.
