Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 66 / 1 / ii / Solution

By spectral decomposition, the Von Neumann entropy is the Shannon entropy of the eigenvalues:Throughout, logarithms have base two, so the Von Neumann entropy and Shannon entropy are measured in bits. The continuous convention $0{\log }_{2}0=0$ includes zero eigenvalues.