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Gaussian states and Gaussian transformations represent an interesting counterpart to two-level systems in quantum optics, on the one hand easily described using first and second moments of quadrature operators and on the other hand simple to implement experimentally using linear optics and optical parametric amplifiers. Here, we propose and analyse protocols for manipulation of entangled Gaussian states of light using local operations and classical communication. Firstly, we study entanglement concentration based on photon subtraction enhanced by local coherent displacements for states in the form of a single-mode squeezed vacuum state split on a beam splitter. We show that coherent displacements can enhance entanglement concentration based on photon subtraction.
Secondly, we study transformations of multipartite permutation invariant Gaussian states. We investigate how entanglement classification is changed by these transformations. In addition, as a figure of merit characterising the quality of the entanglement, we use fidelity of assisted quantum teleportation. We study two different strategies to achieve this objective. The first one is based on adding correlated noise to each mode while the other employs partial non-demolition measurements.