Minimum-error discrimination between mixed quantum states

We derive a general lower bound on the minimum-error probability for ambiguous discrimination between arbitrary m’s mixed quantum states with given prior probabilities. When m = 2, this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. In particular, we show necessary and sufficient conditions on the minimum-error probability for ambiguous discrimination of mixed quantum states attaining this lower bound derived. Then, under a certain condition, we compare the relation between the minimum-error probability for ambiguously discriminating arbitrary m’s mixed quantum states and the optimal failure probability for unambiguously discriminating the same states. When m = 2, this relation has been proved by Herzeg and Bergou. PACS numbers: 03.67.-a, 03.65.Ta