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2

If you are happy with Bob being right only in some percentage of the cases, there is a much easier protocol which does not even require entanglement: Just let Bob guess Alice's bits. He will be right in 50% of the cases. Note that once the probability to guess the right result is above 50%, communication is possible, e.g. by doing majority voting. In ...

20

This is really a subtle point. You are right that in 25% of the cases, Bob will randomly chose the "correct" measurement basis and thus get the correct value. However, there is no way for Bob to know when he has actually chosen the right basis and when he has chosen the wrong basis, so his measurement outcome does not contain more information that a random ...

3

The short answer is special relativity. classically According to classical mechanics, there is nothing to prevent an object from accelerating faster than the speed of light. By conservation of energy you can calculate the speed of a dropped object by looking at the change in gravitational potential. As you note, the equation $PE=mgh$ needs to be modified ...

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