The paper estimates the Chernoff rate for the efficiency of quantum hypothesis testing. For both joint and separate measurements, approximate bounds for the rate are given if both states are mixed, and exact expressions are derived if at least one of the states is pure. The efficiencies of tests with separate and joint measurements are compared. The results are illustrated by a test of quantum entanglement.
"On the Chernoff bound for efficiency of quantum hypothesis testing." Ann. Statist. 33 (2) 959 - 976, April 2005. https://doi.org/10.1214/009053604000001219