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 $\backslash rho\_\{AB\}\; =|\backslash Psi\backslash rangle\backslash langle\backslash Psi|\_\{AB\}$, it is given by: :$\backslash mathcal\{E\}(\backslash rho)\; \backslash equiv\; \backslash mathcal\{S\}(\backslash rho\_A)\; =\; \backslash mathcal\{S\}(\backslash rho\_B)$, where $\backslash rho\_A=\backslash textrm\{Tr\}\_\{B\}(|\backslash Psi\backslash rangle\backslash langle\backslash Psi|)$ and $\backslash rho\_B=\backslash textrm\{Tr\}\_\{A\}(|\backslash Psi\backslash rangle\backslash langle\backslash Psi|)$. Many entanglement measures reduce to the entropy of entanglement when evaluated on pure states. Among those are * [[Distillable entanglement]] * [[Entanglement cost]] * [[Entanglement of formation]] * [[Relative entropy of entanglement]] * [[Squashed entanglement]] Some entanglement measures that do not reduce to the entropy of entanglement are * [[Negativity]] * [[Logarithmic negativity]] * [[Robustness of entanglement]] == See also == * [[Quantum relative entropy]] [[Category:Entropy]] [[Category:Handbook of Quantum Information]] [[Category:Entanglement]]