Effects of decoherence and errors on Bell-inequality violation

We study optimal conditions for violation of the Clauser-Horne-Shimony-Holt form of the Bell inequality in the presence of decoherence and measurement errors. We obtain all detector configurations providing the maximal Bell inequality violation for a general (pure or mixed) state. We consider local decoherence which includes energy relaxation at the zero temperature and arbitrary dephasing. Conditions for the maximal Bell-inequality violation in the presence of decoherence are analyzed both analytically and numerically for the general case and for a number of important special cases. Combined effects of measurement errors and decoherence are also discussed.