Quantum measurement for a group-covariant state set
Kenji Nakahira, Tsuyoshi Sasaki Usuda · Physical Review A · 2013
We consider a group covariant quantum state set with a group in which each element corresponds to a unitary or antiunitary operator. This type of quantum state set can express a broad class of quantum state sets, including geometrically uniform state sets and self-symmetric state sets. We derive that for any quantum measurement for a group-covariant state set (both with and without a certain fraction of inconclusive results), a group covariant quantum measurement exists with respect to the same group with the same performance, that is, the same probability of correct detection and the same rate of inconclusive results. We then show that a group covariant optimal measurement exists for any group-covariant state set. In some cases, we derive an optimal measurement for a group-covariant state set.