ON STATE-DEPENDENT IMPLICATION IN QUANTUM-MECHANICAL DISTANT CORRELATIONS

Let rho(12) be an arbitrary given composite-system state (statistical operator). It is shown that same-subsystem events imply each other sta te-dependently according to rho(12) if and only if they act equally in the range of the corresponding subsystem state (reduced statistical o perator). Opposite-subsystem events imply each other in the same way i f and only if they are twin events, i.e. E(1 rho 12) = F-2 rho 12 If r ho(12) is a pure state, it is shown that the anti-unitary correlation operator also plays a decisive role in the latter implication.