On state-dependent implication in quantum-mechanical distant correlations

Let ρ12 be an arbitrary given composite-system state (statistical operator). It is shown that same-subsystem events imply each other state-dependently according to ρ12 if and only if they act equally in the range of the corresponding subsystem state (reduced statistical operator). Opposite-subsystem events imply each other in the same way if and only if they are twin events, i.e. E1ρ12=F2ρ12. If ρ12 is a pure state, it is shown that the anti-unitary correlation operator also plays a decisive role in the latter implication. (author)