Physics 4999E Study Guide - Final Guide: Quantum Relative Entropy, Density Matrix, Qubit

• School: Western University
• Department: Physics
• Course: Physics 4999E
• Professor: john stockholm

Document Summary

Cs 766/qic 820 theory of quantum information (fall 2011) Lecture 10: continuity of von neumann entropy; quantum relative entropy. In the previous lecture we de ned the shannon and von neumann entropy functions, and es- tablished the fundamental connection between these functions and the notion of compression. In this lecture and the next we will look more closely at the von neumann entropy in order to establish some basic properties of this function, as well as an important related function called the quantum relative entropy. The rst property we will establish about the von neumann entropy is that it is continuous everywhere on its domain. First, let us de ne a real valued function : [0, ) r as follows: ( ) = (cid:26) ln( ) > 0. This function is continuous everywhere on its domain, and derivatives of all orders exist for all positive real numbers.