Quantum Entropy and Quantum Channel

Abstract

In this section, we discuss the entropy in usual quantum dynamical systems (QDS for short) described by Hilbert space terminology. A formulation of quantum mechanical entropy, started by Von Neumann around 1930, 20 years ahead of Shannon, now becomes a fundamental tool to analyze physical phenomena. Von Neumann entropy is defined for a density operator (state) ρ ∈ S(H), the set of all density operators on a Hilbert space H, by

$$S(\rho ) = - {\text{tr}}\rho {\text{ log}}\rho .$$

(3.1)