Quantum Sufficiency in the Operator Algebra Framework

The paper is devoted to the investigation of the notion of sufficiency in quantum statistics. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), Petz’s sufficiency, and Umegaki’s sufficiency. The problem of the existence and structure of the minimal sufficient subalgebra is analyzed in some detail, conditions yielding equivalence of the three modes of sufficiency are considered, and quantum Basu’s theorem is obtained. Moreover, it is shown that an interesting “factorization theorem” of Jenčová and Petz needs some corrections to hold true

Anthropological characteristics of a case of microcephaly

The article describes a female skull from the contemporary cementary of Pestkovo, Bulgaria, with morphological traits of microcephaly (skull capacity - 907 cm3 ). The skull was characterised by means of measurements with reference to 60 skulls of contemporary Bulgarians. Thus the normalised data and values of natural Perkal’s indices were obtained. Obtained data indicate morphological differences of skull with microcephaly compared with the normal ones. In general, the analysed skull is of a smaller size although the values of its height (porion-bregma), total facial height (nasiongnathion) and palatial length (orale-staphylion) are bigger than in the control group

Cloning by positive maps in von Neumann algebras

We investigate cloning in the general operator algebra framework in arbitrary dimension assuming only positivity instead of strong positivity of the cloning operation, generalizing thus results obtained so far under that stronger assumption. The weaker positivity assumption turns out quite natural when considering cloning in the general C∗-algebra framework