Bayesian inference in quantum systems

Bayes criteria are explicitly applied to statistical decision problems in simple quantum mechanical systems. The minimum Bayes cost is calculated for systems including polarised spins and relativistic spin 12 particles. The results suggest that, in decisions for a given ensemble of particles, on the average, the Bayes cost almost always decreases if one treats the ensemble as a single composite system instead of performing separate measurements on the individual particles. The optimal average sample size in observing spin 12 particles is also derived. These results are potentially relevant to experimental design.