Semidefinite Programming in Quantum Information Science

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum information science. Following a review of the theory of semidefinite programming, the book proceeds to describe how it can be used to address a wide range of important problems from across quantum information science. Specific applications include quantum state, measurement, and channel estimation and discrimination, entanglement detection and quantification, quantum distance measures, and measurement incompatibility. Though SDPs have become an increasingly important tool in quantum information science it's not yet the kind of mathematics students learn routinely. Assuming only a basic knowledge of linear algebra and quantum physics and quantum information, this graduate-level book provides a unified and accessible presentation of one of the key numerical methods used in quantum information science. Whilst the focus is on the theoretical machinery of SDPs, the authors have provided an accompanying GitHub repository containing example code, covering some of the SDPs studied in this book.

Key features

• Accessible for graduate students in science and mathematics

• A unified and accessible presentation of one of the key numerical methods used in quantum information science

• Written by leading researchers on the topic

• Accompanying GitHub repository with sample code

半定規劃（SDP）是一類在物理、工程和數學等多個領域中應用的優化問題。半定規劃特別適用於量子物理和量子信息科學中的問題。本書在回顧半定規劃理論後，描述了如何應用它來解決量子信息科學中的一系列重要問題。具體應用包括量子狀態、測量和通道估計與區分、純化度檢測和量化、量子距離度量以及測量不相容性。儘管半定規劃在量子信息科學中已成為一種越來越重要的工具，但它還不是學生們常常學習的數學方法。本書假設讀者只具備基本的線性代數、量子物理和量子信息的知識，提供了一個統一且易於理解的研究半定規劃在量子信息科學中使用的關鍵數值方法的研究生級別的教材。雖然重點是半定規劃的理論工具，但作者還提供了一個附帶的GitHub存儲庫，其中包含本書研究的一些半定規劃的示例代碼。

主要特點：
- 適合科學和數學研究生閱讀
- 提供了一個統一且易於理解的研究半定規劃在量子信息科學中使用的關鍵數值方法的教材
- 由該領域的領先研究人員撰寫
- 附帶GitHub存儲庫，包含示例代碼