Abstract
Let be an arbitrary given composite-system state (statistical operator). It is shown that same-subsystem events imply each other state-dependently according to 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. . If is a pure state, it is shown that the anti-unitary correlation operator also plays a decisive role in the latter implication.
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