About optimal measurements in quantum hypothesizes testing

Abstract

We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which considers the pair as one system) cannot be less optimal than the corresponding sequential one (local measurements, accompanying by transfer of classical information). The case of equality is achieved only when the mixed states have the same eigenvalues or the same eigenvectors. Further, we consider a case then the two systems are entangled: measurement of one system induces a reduction of the another one's state. The conclusion about optimal character of combined measurement takes place again, and conditions where the above-mentioned methods coincide are derived.