Physics 4999E Final: 11

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

Document Summary

Cs 766/qic 820 theory of quantum information (fall 2011) Lecture 11: strong subadditivity of von neumann entropy. In this lecture we will prove a fundamental fact about the von neumann entropy, known as strong subadditivity. Let us begin with a precise statement of this fact. Theorem 11. 1 (strong subadditivity of von neumann entropy). For every state d (x y z ) of these registers it holds that. S(x, y, z) + s(z) s(x, z) + s(y, z). There are multiple known ways to prove this theorem. The approach we will take is to rst establish a property of the quantum relative entropy, known as joint convexity. Once we establish this property, it will be straightforward to prove strong subadditivity. 11. 1 joint convexity of the quantum relative entropy. We will now prove that the quantum relative entropy is jointly convex, as is stated by the follow- ing theorem. Theorem 11. 2 (joint convexity of the quantum relative entropy).