Bayes-cost reduction algorithm in quantum hypothesis testing (Corresp.)

An iterative procedure is described for reducing the Bayes cost in decisions among
M>2
quantum hypotheses by minimizing the average cost in binary decisions between all possible pairs of hypotheses: the resulting decision strategy is a projection-valued measure and yields an upper bound to the minimum attainable Bayes cost. From it is derived an algorithm for finding the optimum measurement states for choosing among
M
linearly independent pure states with minimum probability of error. The method is also applied to decisions among
M
unimodal coherent quantum signals in thermal noise.