Quantum Information Theory: Mathematical Foundation (Hardcover)

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides  lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption.
Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation.
With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained.
Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information.
To aid in understanding, each chapter is accompanied by a set of exercises and solutions.

這本研究生教科書提供了量子資訊理論的統一觀點。它清楚地解釋了必要的數學基礎，並將信息理論和量子力學的關鍵主題融合在一起，並提供了基本結果的清晰解釋。由於這種統一的方法，它使得量子通信中的高級主題，如量子傳輸、超密碼、量子狀態傳輸（量子錯誤修正）和量子加密變得容易理解。

自前一本書《量子資訊：一個介紹》出版以來，量子資訊領域取得了巨大的進展。特別是以下主題 - 在這裡都有涉及 - 取得了重大進展：量子狀態區分、量子通道容量、雙方和多方纏繞、量子通信的安全分析、反向Shannon定理和不確定性關係。

關於量子安全性的分析，本書採用了一種改進的方法來評估洩漏的信息，並確定了量子安全性和量子相干之間的顯著關係。這兩個改進結合在一起，使得對量子狀態傳輸的分析更加精確。此外，還解釋了各種新發現的不確定性關係的類型。

本書介紹了大量的新發展，使讀者了解量子資訊領域的最新進展和挑戰。

為了幫助理解，每章附有一組練習題和解答。