Von Neumann entropy

The '''von Neumann entropy''' of a quantum state $\backslash rho$ is given by the formula, :$\backslash mathcal\{S\}(\backslash rho)\; \backslash equiv\; -\backslash textrm\{Tr\}(\backslash rho\; \backslash log\; \backslash rho)$ and if $\backslash lambda\_i$ are the eigenvalues of $\backslash rho$ then the Von Neumann entropy can be reexpressed as: :$\backslash mathcal\{S\}(\backslash rho)=-\backslash sum\_i\; \backslash lambda\_i\; \backslash log\; (\backslash lambda\_i).$ In quantum information the logarithms are usually taken to be base 2, giving a maximum entropy of 1 for a [[qubit]]. == See also == * [[Quantum relative entropy]] [[Category:Entropy]] [[Category:Handbook of Quantum Information]]