Ulrike Herzog - Optimal strategies for the discrimination of quantum states
Quantum state discrimination is the task to determine the actual state of a quantum system prepared with a given prior probability in one of N given states, where the states can be pure or mixed. Since nonorthogonal quantum states cannot be distinguished perfectly, discrimination strategies have been developed that are optimized with respect to various criteria. The measurements performing the strategies are often generalized measurements, requiring in many cases a certain probability of getting an inconclusive outcome.
The talk gives an overview on different strategies for state discrimination and their mutual relations. The focus is on the specific measurement that discriminates the states with the maximum overall probability of correct results, while the probability of inconclusive results is fixed at a given value. When the fixed value increases, starting from zero, the optimum measurement interpolates between minimum-error discrimination and a measurement that under certain conditions corresponds to the strategy of optimal maximum-confidence discrimination, or of optimum unambiguous discrimination, respectively. As illustrative examples, explicit solutions are derived for the discrimination of qubit states that are partially symmetric in the sense that they fall into two groups, where within each group they are symmetric and equiprobable.