量子统计推断的充分性
Sufficiency in quantum statistical inference
摘要：
本文试图在非交换代数的背景下发展一个与经典数理统计思想相平行的充分性理论。粗粒化的充分性意味着提取关于给定状态族的相互关系的所有信息。本文用几种等价的方法刻画了充分粗粒化，并得到了因子分解定理的非交换类比。在应用中的等式的情况下，强次可加性的冯诺伊曼熵，Imoto-Koashi定理和指数族的治疗。该文件的设置允许潜在的希尔伯特空间是无限维的。
英文摘要：
This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative analogue of the factorization theorem is obtained. Among the applications the equality case for the strong subadditivity of the von Neumann entropy, the Imoto-Koashi theorem and exponential families are treated. The setting of the paper allows the underlying Hilbert space to be infinite dimensional.
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