Hi :-) I'm working on my master thesis in the field of quantum theory; currently I investigante No-Go-Theorems like the No-Cloning, No-Deleting, No-Hiding, No-Communication-Theorems ans so on. There is a fundamental question wich is somehow linked to the No-Communication-Theorem. Is it - in theory - possible to measure one qubits multiple times? Lets say, you have a qubit |q> = |+> = 0.5^0.5 * |0> + 0.5^0.5 * |1> and perform a measurement in the standard basis. With a probability of 0.5 the outcome of the measurement is |0>. Since the superpostition is destroyed now, the outcome of a second, third, fourth... measurement must be |0> as well. But is it even allowed to perform multiple measurements? I'm aware that this might be difficult to realize, since photons are destroyed during a measurment. I'm wondering if the theory of quantum mechanics prohibits multiple measurements. These are my thoughts wich lead to a contradiction to the No-Communication-Theorem, so somewhere must be a mistake: If I take a qubit |q> = |+> and perform a measurement in the |+>/|-> basis, the outcome would be |+> with probabilty 1. By doing this I fix the qubit in the state |+>. So if it would be possible to perform another measurement in the |0>/|1> basis I would get a random bit. And since |q> is fixed in the state |+>, every following measurement should producea random bit as well. The No-Communication-Theorem says that it is impossible to communicate via entagled EPR-pairs, especially not faster than light. But if there would be a pair of entagled qubits - one on earth, one on Mars - and the first one is measured in either the |0>/|1> basis or the |+>/|-> basis, then the person on mars would be able to find out wich basis was used by performing multiple measurements in both basises; for one basis he always gets the same result, for the other basis he gets different results. So... this is known to be impossible. Maybe the answer is just, that not even in theory it is possible to perform multiple measurements on one qubit, but I never heard or read about such a limitation.