Fundamental limitations to key distillation from Gaussian states with Gaussian operations

We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using local operations, classical processing, and public communication. For one-way communication or when two-way is allowed but Alice Bob first perform destructive measurements, we prove bounded R\'enyi-2 entanglement formation ${E}_{F,2}^{\mathrm{G}}$. The saturation this inequality for pure provides an operational interpretation entropy as rate accessible with operations In general setting arbitrary interactive protocols, argue $2{E}_{F,2}^{\mathrm{G}}$ still serves bound extractable key. conjecture factor 2 spurious, suggesting ${E}_{F,2}^{\mathrm{G}}$ coincides under measurements use these results to a gap between rates obtainable versus operations. This observed produced sending one half two-mode squeezed vacuum through loss channel, in regime sufficiently low squeezing high transmissivity. Finally, wide class states, including all recently proposed equality intrinsic entanglement. unified quantifier emerging such then endowed direct value teleportation game.