量子理论数学概念指南
Guide to Mathematical Concepts of Quantum Theory
摘要：
量子理论是近百年来发展起来的现代科学的支柱之一。在这篇评论文章中，我们介绍，一步一步，量子理论理解为一个数学模型描述量子实验。我们首先将实验分为两个部分：准备过程和测量过程，从而记录特定的结果。实验的这两个成分分别由状态和效应表示。此外，整个量子测量的图片将被开发和概念的观测，仪器和测量模型代表三种不同的描述实验将被介绍。在第二阶段，我们通过引入量子信道的概念来描述系统在制备和测量之间的变化，从而丰富了实验模型。最后，我们回顾了量子纠缠的基本性质。正文包含许多例子和练习也包括许多题目从量子信息理论和量子测量理论。目标是对量子理论的现代语言的主要概念给出一个数学上清晰和自足的解释。
英文摘要：
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory.
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