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This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated paralelly to the the mea- sure theoretic case. It turns out that several classical examples and results have a non-commutative analogue. Some of the results are presented with- out proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.

SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES