Guide to mathematical concepts of quantum theory

Q4 Physics and Astronomy

Acta Physica Slovaca Pub Date : 2008-08-01 DOI:10.2478/v10155-010-0091-y

Teiko Heinosaari, M. Ziman

{"title":"Guide to mathematical concepts of quantum theory","authors":"Teiko Heinosaari, M. Ziman","doi":"10.2478/v10155-010-0091-y","DOIUrl":null,"url":null,"abstract":"Quantum Theory is one of the pillars of modern science\ndeveloped over the last hundred years. In this review paper we\nintroduce, step by step, the quantum theory understood as a\nmathematical model describing quantum experiments. We start\nwith splitting the experiment into two parts: a preparation\nprocess and a measurement process leading to a registration of\na particular outcome. These two ingredients of the experiment\nare represented by states and effects, respectively. Further,\nthe whole picture of quantum measurement will be developed and\nconcepts of observables, instruments and measurement models\nrepresenting the three different descriptions on experiments\nwill be introduced. In the second stage, we enrich the model of\nthe experiment by introducing the concept of quantum channel\ndescribing the system changes between preparations and\nmeasurements. At the very end we review the elementary\nproperties of quantum entanglement. The text contains many\nexamples and exercises covering also many topics from quantum\ninformation theory and quantum measurement theory. The goal is\nto give a mathematically clear and selfcontaining explanation\nof the main concepts of the modern language of quantum theory.","PeriodicalId":50886,"journal":{"name":"Acta Physica Slovaca","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/v10155-010-0091-y","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Physica Slovaca","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/v10155-010-0091-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Physics and Astronomy","Score":null,"Total":0}

引用次数: 17

Abstract

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 exercises covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and selfcontaining explanation of the main concepts of the modern language of quantum theory.

查看原文本刊更多论文

量子理论的数学概念指南

量子理论是近百年来发展起来的现代科学的支柱之一。在这篇综述文章中，我们一步一步地介绍量子理论，将其理解为描述量子实验的数学模型。我们首先将实验分为两个部分:准备过程和测量过程，导致特定结果的注册。实验的这两个成分分别用状态和效应来表示。此外，将发展量子测量的全貌，并介绍代表三种不同实验描述的可观测物、仪器和测量模型的概念。在第二阶段，我们通过引入量子通道的概念来丰富实验模型，描述系统在准备和测量之间的变化。最后我们回顾了量子纠缠的基本性质。本文包含许多例子和练习，涵盖了量子信息理论和量子测量理论的许多主题。我们的目标是对现代量子理论语言的主要概念给出一个数学上清晰且自包含的解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Physica Slovaca 物理-物理：综合

CiteScore

0.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： acta physica slovaca is an internationally recognised physics journal originally established in 1950. Since 1998 listed in Current Contents. Since 2006, acta physica slovaca publishes review and tutorial articles. Papers written by specialists in a given field are intended to be accessible also to non-specialists and PhD students. Although the printed version of the journal is available, all issues are free to download from the journal''s web page. We hope that the new issues of acta physica slovaca will be useful and interesting for readers.