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


See also