Lower bounds on the entanglement of formation for general Gaussian states

Abstract

We derive two lower bounds on entanglement of formation for arbitrary mixed Gaussian states by two distinct methods. To achieve the first one we use a local measurement procedure derived by Giedke et al [Quantum Inf. and Comp. vol.1, 79 (2001)] that symmetrizes a general Gaussian state and the fact that entanglement cannot increase under local operations and classical communications. The second one is obtained via a generalization to mixed states of an interesting result derived by Giedke et al [quant-ph/0304042], who show that squeezed states are those that, for a fixed amount of entanglement, maximize Einstein-Podolsky-Rosen-like correlations.