  We investigate localization of entanglement of multipartite mixed Gaussian
states into a pair of modes by local Gaussian measurements on the remaining
modes and classical communication. We provide a detailed proof that for
arbitrary symmetric Gaussian state maximum entanglement can be localized by
homodyne detection of either amplitude or phase quadrature on each mode. We
then consider arbitrary mixed three-mode Gaussian states and show that the
optimal Gaussian measurement on one mode yielding maximum entanglement among
the other two modes can be determined by calculating roots of a high-order
polynomial. Finally, we discuss localization of entanglement with single-photon
detection.
