Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality

We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) on a class of entangled generalized Werner states, thus demonstrating that such measurements do not always violate a Bell-type inequality. We also show that, in general, if the state ${\rho }^{\prime }$ can be obtained from $\rho$ with certainty by local quantum operations without classical communication, then an LHVPOV model for the state $\rho$ implies the existence of such a model for ${\rho }^{\prime }.$