Selected Advances in Quantum Shannon Theory

Quantum Information Chapter 10. Quantum Shannon Theory

Contents 10 Quantum Shannon Theory 1 10.1 Shannon for Dummies 2 10.1.1 Shannon entropy and data compression 2 10.1.2 Joint typicality, conditional entropy, and mutual information 6 10.1.3 Distributed source coding 8 10.1.4 The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1 Mathematical properties of H(ρ) 18 10.2.2 Mixing, measurement, and entropy 20 10.2.3 Strong subadditivit...

From Classical to Quantum Shannon Theory

The aim of this book is to develop"from the ground up"many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entangl...

Problems for : Selected Topics in Quantum Theory

A set of problems is offered to accompany the set of lectures with the above title. Topic 1: Coherent States 1.1 Let {|n〉}, n = 0, 1, 2, 3, . . ., denote a complete set of orthonormal vectors in an abstract Hilbert space , with 〈m|n〉 = δmn. Next, let |χ〉 = √ 1 − |χ|2 |0〉 + χ|1〉 , for all complex χ, 0 ≤ |χ| ≤ 1, denote a family of two-dimensional vectors. a) If χ→ χ in the sense of complex numbe...

Quantum Reverse Shannon Theorem

Shannon Wavelets Theory

Shannon wavelets are studied together with their differential properties known as connection coefficients . It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of L2 R functions. The differential properties of Shannon wave...