  We propose upper and lower bounds on the maximum success probability for
discriminating given quantum states. The proposed upper bound is obtained from
a suboptimal solution to the dual problem of the corresponding optimal state
discrimination problem. We also give a necessary and sufficient condition for
the upper bound to achieve the maximum success probability; the proposed lower
bound can be obtained from this condition. It is derived that a slightly
modified version of the proposed upper bound is tighter than that proposed by
Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and
lower bounds on the maximum success probability with a fixed rate of
inconclusive results. The performance of the proposed bounds are evaluated
through numerical experiments.
