The quantum no-cloning theorem states that one cannot "build" a perfect cloning device for arbitrary quantum systems.
There also exists a famous thought experiment where Alice transmits information to Bob super-luminously using a quantum cloning device, which is resolved by the no-clone theorem. Essentially, there is an electron-positron pair in the singlet state. The positron travels to Alice, the electron to Bob. If Alice measures the positron in the spin down direction, Bob makes a lot of copies of the electron using a cloning device, and then measures them. If he gets all spin up, he knows Alice made the measurement. If he gets a 50-50 mix, he knows Alice did not make the measurement. If he does this fast enough, and Alice is far enough away, one might consider that information has travelled faster than the speed of light.
However, the cloning device he makes is restricted to be able to perfectly clone only plus and minus states, and fails to clone arbitrary linear combinations, i.e his device could not reproduce the electron-half of the singlet state if Alice did not make a measurement.
Here is my question. What if Bob just says, if I get all the same answer, she made the measurement, which is possible because his cloning device can clone states in either the up or down state, just not a linear combination. If he gets ANY mixture at all, he says she did not make the measurement. Why does the no-clone theorem prevent this, and why is this not a violation of prohibited super-luminal information travel?
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