Randomness, nonlocality, and information in entangled correlations

It is shown that the Einstein-Podolsky-Rosen (EPR) correlations for arbitrary spin s and the Greenberger-Horne-Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the information Bell inequalities. Relations between the randomness, the nonlocality, and the entropic information for the EPR and the GHZ correlations are established and discussed.