  Entangled two-mode Gaussian states are a key resource for quantum information
technologies such as teleportation, quantum cryptography and quantum
computation, so quantification of Gaussian entanglement is an important
problem. Entanglement of formation is unanimously considered a proper measure
of quantum correlations, but for arbitrary two-mode Gaussian states no
analytical form is currently known. In contrast, logarithmic negativity is a
measure straightforward to calculate and so has been adopted by most
researchers, even though it is a less faithful quantifier. In this work, we
derive an analytical lower bound for entanglement of formation of generic
two-mode Gaussian states, which becomes tight for symmetric states and for
states with balanced correlations. We define simple expressions for
entanglement of formation in physically relevant situations and use these to
illustrate the problematic behavior of logarithmic negativity, which can lead
to spurious conclusions.
