Название: Quantum Information Theory: Concepts and Methods
Автор: Joseph M. Renes
Издательство: De Gruyter
Год: 2022
Страниц: 336
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

If the carriers of information are governed by quantum mechanics, new principles for information processing apply. This graduate textbook introduces the underlying mathematical theory for quantum communication, computation, and cryptography. A focus lies on the concept of quantum channels, understanding fi gures of merit, e.g. fidelities and entropies in the quantum world, and understanding the interrelationship of various quantum information processing protocols.

The first part covers the formalism of quantum information theory, or really open quantum systems of finite dimension, developing it by explicit analogy with classical probability theory. The second part deals with the tools useful for analyzing information processing tasks, most of which also find application in other parts of the field. Characteristic of Part II is a heavy reliance, if not overreliance, on semidefinite programming to phrase and derive most of the main results. I have attempted to keep the required background for the reader to a modest level—a thorough understanding of linear algebra—and then to derive everything from there. The third part takes up the information processing protocols themselves, with the particular emphasis on so-called “one-shot” statements of structureless resources. These statements are formulated in terms of a quantity involved in the simpler task of binary hypothesis testing. From there, results for the usual setting of i. i. d. resources can be recovered by Stein’s lemma relating hypothesis testing to entropy. This is also quite at odds with most texts on information theory, which places entropy front and center, even treating it axiomatically. Again, I follow the strictly operational approach. My aim here has also been to keep the number of different tools developed in Part II and techniques employed in Part III to a minimum.