Some features of the notion of sufficiency in quantum statistics are investigated. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), strong sufficiency and Umegaki’s sufficiency. It is shown that for a finite von Neumann algebra with a faithful family of normal states the minimal sufficient von Neumann subalgebra is sufficient in Umegaki’s sense. Moreover, a proper version of the factorization theorem of Jenčová and Petz is obtained. The structure of the minimal sufficient subalgebra is described in the case of pure states on the full algebra of all bounded linear operators on a Hilbert space.

中文翻译：

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有限和完全冯诺依曼代数的量子充分性的一些方面

研究了量子统计中充分性概念的一些特征。考虑了三种这种概念：普通充足（简称：充足）、强充足和梅垣充足。结果表明，对于具有忠实正规态族的有限冯诺依曼代数，在梅垣的意义上，最小充分冯诺依曼子代数是充分的。此外，还获得了 Jenčová 和 Petz 的分解定理的正确版本。在希尔伯特空间上所有有界线性算子的全代数上的纯态的情况下描述了最小充分子代数的结构。