Threshold bounds for noisy states

For a nonseparable bipartite quantum state violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, we evaluate amounts of noise breaking a quantum character of its statistical correlations under any generalized quantum measurements of Alice and Bob. Expressed in terms of the reduced states, these new threshold bounds can be easily calculated for any concrete state. The threshold noisy state, not violating the extended CHSH inequality and the perfect correlation form of the Bell inequality, does not necessarily either admit a local hidden variable model or exhibit Bell's perfect correlations. We consider examples and, in particular, demonstrate separable noisy states that do not violate the perfect correlation form of the original Bell inequality and have negative correlation functions