Noise Robustness of the Nonlocality of Entangled Quantum States

We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state $\rho$ of two $d$-dimensional systems and completely depolarized noise, with respective weights $p$ and $1-p$. We first construct a local model for the case in which $\rho$ is maximally entangled and $p$ at or below a certain bound. We then extend the model to arbitrary $\rho$. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements, the critical value of the noise parameter $p$ for which the state becomes local is at least asymptotically $\log (d)$ larger than the critical value for separability.