# Entropy of entanglement

The entropy of entanglement is an entanglement measure for a bipartite pure states. It is defined as the von Neumann entropy of one of the reduced states. That is, for a pure state $\rho_{AB} =|\Psi\rangle\langle\Psi|_{AB}$, it is given by:

$\mathcal{E}(\rho) \equiv \mathcal{S}(\rho_A) = \mathcal{S}(\rho_B)$,

where $\rho_A=\textrm{Tr}_{B}(|\Psi\rangle\langle\Psi|)$ and $\rho_B=\textrm{Tr}_{A}(|\Psi\rangle\langle\Psi|)$.

Many entanglement measures reduce to the entropy of entanglement when evaluated on pure states. Among those are

Some entanglement measures that do not reduce to the entropy of entanglement are