Counter-factual Processes in Quantum Mechanics

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The counter-intuitive phenomena in quantum mechanics are often based on the counter-factual (or virtual) processes. The famous example is the Hardy paradox, which has been recently solved in two independent experiments. Also, the delayed choice experiment and one of quantum descriptions of the closed time like curves can be also examples of the counter-intuitive phenomena. The counter-factual processes can be characterized by the weak value initiated by Yakir Aharonov and his colleagues. In this talk, I will introduce the weak value from the probability theory and the connection to the counter-factual processes in these examples.