The Functional Analysis of Quantum Information Theory: A Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter (Lecture Notes in Physics)
暫譯: 量子資訊理論的函數分析:基於Gilles Pisier、K. R. Parthasarathy、Vern Paulsen和Andreas Winter講座的筆記集(物理學講義筆記)
Ved Prakash Prakash Gupta
- 出版商: Springer
- 出版日期: 2015-06-10
- 售價: $2,230
- 貴賓價: 9.5 折 $2,119
- 語言: 英文
- 頁數: 152
- 裝訂: Paperback
- ISBN: 3319167170
- ISBN-13: 9783319167176
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相關分類:
物理學 Physics、量子 Quantum
海外代購書籍(需單獨結帳)
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商品描述
This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.
商品描述(中文翻譯)
這本書為讀者提供了對運算子代數及其推廣、運算子空間和運算子系統的當前研究的簡明介紹,特別關注它們在量子資訊科學中的應用。這一數學框架可追溯至約翰·馮·諾伊曼(John von Neumann)的數學工作,他是運算子代數的先驅之一,這些工作構成了當前大多數量子理論數學處理的基礎,並且是二十世紀函數分析中最具活力的領域之一。如今,馮·諾伊曼的遠見在快速增長的量子資訊理論領域中得到了體現。這些筆記彙集了幾年前在印度金奈的IMSc舉辦的一組非常傑出的數學家和量子資訊理論家的講座內容,並且特別注意將材料呈現為該主題的入門書。從運算子空間和運算子系統的基本定義開始,這本書接著討論了幾個重要的定理,包括斯廷斯普林(Stinespring)的完全正映射的擴張定理和基爾希伯格(Kirchberg)關於C*-代數的張量積的定理。它還更深入地探討了運算子系統的抽象特徵,並根據量子資訊理論中不同張量積的需求,詳細討論了運算子系統中的張量積理論。在量子資訊方面,本書對雙部分量子系統中糾纏的量化進行了嚴謹的處理,並回顧了四個不同的領域,其中運算子系統和運算子代數理論的思想發揮了自然的作用:量子通道上的零錯誤通信問題、量子熵的強子加性性質、量子狀態上的不同範數及其對應的量子通道上的誘導範數,最後,還探討了矩陣值隨機變量在量子資訊環境中的應用。