In various branches of quantum theory such as quantum information processing, quantum communication theory or quantum statistics one of the basic problems is to determine the state of a given quantum system. In the simplest case there is a finite set of states specifying the possible preparation of the quantum system. In the Bayesian approach of quantum statistics, the likelihood of the different states is determined by an a priori probability distribution. One makes a decision in favor of one of the states following a specified rule based on the outcomes of a generalized measurement -called a quantum test. In the binary case optimal tests, i.e. tests minimizing the averaged probability of rejecting the true state, are known to be given by Holevo-Helstrom projections. These generalize the classical likelihood ratio tests. Here we consider the scenario where there is an arbitrarily large finite number n of copies of the quantum system available for performing a measurement. [download]
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