# Von Neumann entropy

The von Neumann entropy of a quantum state ρ is given by the formula,

S(ρ) ≡  − Tr(ρlogρ)

and if λi are the eigenvalues of ρ then the Von Neumann entropy can be reexpressed as:

S(ρ) =  − ∑iλilog(λi).

In quantum information the logarithms are usually taken to be base 2, giving a maximum entropy of 1 for a qubit.