Actually the number of possible states of a single qubit is uncountably infinite (according to quantum mechanics). Of course the number of results of any given complete measurement of that qubit is exactly two, but then, the number of measurements you can do on it is uncountably infinite. In theory, at least. In practice the number may be very high, but certainly finite, because you cannot make your measurement apparatus settings infinitely precise.
Thank you, my mistake seems to be the variation in ways the question can be prepared has no bearing on the count of possible output states.
Is this a better analogy?
I want to add 1 + 1 without revealing to the cloud I don't know what 1 + 1 is fearing I will be rained on if it found out.
My question is prepared with two parameters (1 + x) and (1 + y) where x and y are random numbers I want added.
The random numbers are known only to me and can be as large as ones own imagination almost uncountably infinite.
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