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 in...

‎the number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving gaussian binomial coefficients is presented‎.