  Alternative exact expressions are derived for the minimum error probability
of a hypothesis test discriminating among $M$ quantum states. The first
expression corresponds to the error probability of a binary hypothesis test
with certain parameters; the second involves the optimization of a given
information-spectrum measure. Particularized in the classical-quantum channel
coding setting, this characterization implies the tightness of two existing
converse bounds; one derived by Matthews and Wehner using hypothesis-testing,
and one obtained by Hayashi and Nagaoka via an information-spectrum approach.
