Quantum Nonlocality and Partial Transposition for Continuous-Variable Systems

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti et al., Phys. Rev. Lett. 99, 210405 (2007)]. We prove that any $n$-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.