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On state-dependent implication in quantum-mechanical distant correlations. (English) Zbl 0900.81020
Summary: Let $\rho_{12}$ be an arbitrary given composite-system state (statistical operator). It is shown that same-subsystem events imply each other state-dependently according to $\rho_{12}$ 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. $E_1\rho_{12}= F_2\rho_{12}$. If $\rho_{12}$ is a pure state, it is shown that anti-unitary correlation operator also plays a decisive role in the latter implication.

81P10Logical foundations of quantum mechanics; quantum logic
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