论量子信息论的范畴基础:范畴和Cramer-Rao不等式

IF 1.6 4区物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS

Modern Physics Letters A Pub Date : 2023-08-31 DOI:10.1142/S0217732323500852

Florio M. Ciaglia, F. Cosmo, Laura Gonz'alez-Bravo, Alberto Ibort, G. Marmo

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引用次数: 0

摘要

将Cencov经典推理理论的范畴描述推广到量子系统领域。它为量子信息理论提供了一个新的分类基础，以一种自然的方式包含经典和量子信息理论，同时也允许形式化量子环境的概念。这些思想的第一个应用是通过扩展统计流形的概念来纳入类别，并在这种情况下研究一个可能的、单参数的Cramer-Rao不等式。

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On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality

An extension of Cencov’s categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theory of quantum information that embraces both classical and quantum information theories in a natural way, while also allowing to formalize the notion of quantum environment. A first application of these ideas is provided by extending the notion of statistical manifold to incorporate categories, and investigating a possible, uniparametric Cramer–Rao inequality in this setting.

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来源期刊

Modern Physics Letters A 物理-物理：核物理

CiteScore

3.10

自引率

7.10%

发文量

186

审稿时长

3 months

期刊介绍： This letters journal, launched in 1986, consists of research papers covering current research developments in Gravitation, Cosmology, Astrophysics, Nuclear Physics, Particles and Fields, Accelerator physics, and Quantum Information. A Brief Review section has also been initiated with the purpose of publishing short reports on the latest experimental findings and urgent new theoretical developments.