 If an entangled pure vector state of a pair of quantum systems violates state separability then there are measurements of dynamical variables (one on each subsystem) whose joint quantum probability distribution cannot be expressed as a product of probability distributions for separate measurements of each variable. Quantum theory predicts such a probability distribution for each of many types of spatially separated measurements of variables including spin and polarization components on a pair of entangled physical entities assigned such a state, and many of these distributions have been experimentally verified. If one thought that quantum theory treats each dynamical variable by replacing a precise real value assignment by a probability distribution for the results of measurements of that dynamical variable, one might take this already to violate the real state separability principle. But if one entertains a theory that supplements the quantum state by values of additional “hidden” variables, then the quantum probabilities would be taken to arise from averaging over many distinct hidden states. In that case, it would rather be the probability distribution conditional on a complete specification of the values of the hidden variables that should be taken to specify the underlying chances of system and subsystems exhibiting various possible properties on measurement. The real state might then include all these conditional probability distributions. The best known example of such a theory is the Bohm theory (see the entry on  Bohmian mechanics),  where the “hidden” variables are spatial positions. In each specific experimental context all conditional probabilities are 0 or 1, so the joint conditional probability distributions indeed factorize. But the outcome of a measurement of a chosen dynamical variable on one subsystem depends on what dynamical variable is chosen and measured on the other, no matter just when or how far apart these measurements are selected and made.