In any empirically adequate model of the EPR/B experiment where the pair's state and measurement apparatus settings are the only relevant factors for outcome probabilities, and the quantum-equilibrium distribution is λ-independent, parameter independence implies the failure of controllable probabilistic dependence.
A model or theory that correctly predicts what we actually observe in experiments, even if it might not describe what's 'really' happening underneath.
parameter independence(Used in the context of EPR/B models where the pair's state and apparatus settings are the only relevant factors)
A condition in hidden-variable models under which the probability of a measurement outcome at one wing does not depend on the setting of the apparatus at the other (distant) wing.
quantum equilibrium(quantum physics)
A balanced state in quantum mechanics where particles are distributed in a way that matches all the predictions quantum theory makes about what we'll measure.
λ-independent (lambda-independent)(quantum mechanics and hidden variable theories)
Not depending on a hidden variable (represented by the Greek letter λ) that secretly determines outcomes; in this context, it means the distribution doesn't rely on unknown factors.
Note that the necessary and sufficient conditions for superluminal signaling are different in models that do not exclude in theory the violation of λ-independence. In such models controllable probabilistic dependence is not a necessary condition for superluminal signaling. The reasoning is as follows. Consider any empirically adequate model of the EPR/B experiment in which the pair's state and the settings of the measurement apparatuses are the only relevant factors for the probabilities of meas