Minimum-error discrimination between mixed quantum states

Abstract

We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ 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. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out a upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimum-error probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimum-error probability for {\it ambiguously} discriminating arbitrary $m$ mixed quantum states with the optimal failure probability for {\it unambiguously} discriminating the same states.

A further revised version, and some results have been added

References in corpus (3)

• Unambiguous discrimination of mixed states
• Optimum unambiguous discrimination of two mixed states and application to a class of similar states
• Unambiguous discrimination of mixed states: A description based on system-ancilla coupling

Cited by in corpus (3)

• Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
• Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem
• Minimum-error discrimination of quantum states: New bounds and comparison