Von Neumann entropy

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

\mathcal{S}(\rho) \equiv -\textrm{Tr}(\rho \log \rho)

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

\mathcal{S}(\rho)=-\sum_i \lambda_i \log (\lambda_i).

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

See also

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