On Wandering Subalgebras, Sufficiency and Stroboscopic Tomography

The aim of this paper, the first in the series, is to discuss the relationship between some fundamental statistical concepts for quantum systems described by algebraic methods and the ideas of the so-called stroboscopic tomography, where some geometrical methods are very natural. An example of sufficient conditions which must be fulfilled by sufficient subalgebras that are useful in estimating states of quantum systems are discussed. Subsequent papers in this series will deal with more sophisticated models.