Nonexistence of entangled continuous-variable Werner states with positive partial transpose

Abstract

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.