Optimal POVMs in quantum parameter estimation require at most (dim H)^2 + d(d+1)/2 -1 outcomes for locally unbiased and (dim H)^2 for Bayesian settings, and can be chosen rank-one.
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
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Sufficient support size of measurements for quantum estimation
Optimal POVMs in quantum parameter estimation require at most (dim H)^2 + d(d+1)/2 -1 outcomes for locally unbiased and (dim H)^2 for Bayesian settings, and can be chosen rank-one.