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On state-dependent implication in quantum-mechanical distant correlations. (English) Zbl 0900.81020
Summary: Let ρ 12 be an arbitrary given composite-system state (statistical operator). It is shown that same-subsystem events imply each other state-dependently according to ρ 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 ρ 12 =F 2 ρ 12 . If ρ 12 is a pure state, it is shown that anti-unitary correlation operator also plays a decisive role in the latter implication.
MSC:
81P10Logical foundations of quantum mechanics; quantum logic