  We address an open question about the existence of entangled
continuous-variable (CV) Werner states with positive partial transpose (PPT).
We prove that no such state exists by showing that all PPT CV Werner states are
separable. The separability follows by observing that these CV Werner states
can be approximated by truncating the states into a finite-dimensional convex
mixture of product states. In addition, the constituents of the product states
comprise a generalized non-Gaussian measurement which gives, rather
surprisingly, a strictly tighter upper bound on quantum discord than photon
counting. These results uncover the presence of only negative partial transpose
entanglement and illustrate the complexity of more general non-classical
correlations in this paradigmatic class of genuine non-Gaussian quantum states.
