Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Uhlmann's proof of the Monotonicity of the Relative Entropy

Juan Manuel Pérez-Pardo

Abstract

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful examples are given.

On Uhlmann's proof of the Monotonicity of the Relative Entropy

Abstract

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful examples are given.
Paper Structure (4 sections, 5 theorems, 48 equations)

This paper contains 4 sections, 5 theorems, 48 equations.

Table of Contents

  1. Previous Remarks
  2. Functional Calculus of positive quadratic forms
  3. Interpolation of Quadratic Forms and Relative Entropy
  4. Proof of the monotonicity of the Relative Entropy

Key Result

Theorem 3.4

pusz75 Let $p$ and $q$ be quadratic forms on $\mathcal{V}$ and let $S$ be the space of quadratic forms dominated by $p$ and $q$. The geometric mean of the forms $p$ and $q$ satisfies

Theorems & Definitions (14)

  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Theorem 3.4
  • Proposition 3.5
  • proof
  • Proposition 3.6
  • proof
  • Proposition 3.7
  • proof
  • ...and 4 more