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I'm aware that a qubit can exist in an infinite number of states and that when measured it collapses into one state, with the probability of each state being directly affected by it's latitude.

My question is: Why is this in any way useful? Surely you can't use a unit of information meaningfully when you don't know what it will be..?

Surely, not knowing what a quantum bit is going to be is detrimental to computing? I'm evidently missing something since we know that quantum computing works, but why?

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    $\begingroup$ I suggest taking a look at some quantum algorithms. Qubits are useful since you can use them to solve some computational tasks much faster (apparently) than classical computers, in an asymptotic sense. $\endgroup$ – Yuval Filmus Aug 8 '17 at 10:27
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    $\begingroup$ So you can't find out everything about the value of a qubit. That doesn't mean you know nothing about it. And, sure, quantum computing probably would be more powerful if you could find out everything about the value. But, again, the fact that you can't do everything doesn't mean that you can't do anything. $\endgroup$ – David Richerby Aug 8 '17 at 12:16
  • $\begingroup$ @DavidRicherby I think you misunderstand. How can a piece of information be useful when you have no idea what it will be? $\endgroup$ – Aric Aug 8 '17 at 12:22
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    $\begingroup$ @AricFowler But you do have some idea what it will be: it's drawn from a probability distribution that the algorithm constructed. The algorithm will, presumably, construct a distribution that's quite tightly concentrated about the true answer. And you can always repeat the computation to get multiple samples. $\endgroup$ – David Richerby Aug 8 '17 at 12:40
  • $\begingroup$ @DavidRicherby, that looks like a good answer to me. Want to write that in the answer field? $\endgroup$ – D.W. Aug 8 '17 at 20:35
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So you can't find out everything about the value of a qubit. That doesn't mean you know nothing about it. And, sure, quantum computing probably would be more powerful if you could find out everything about the value. But, again, the fact that you can't do everything doesn't mean that you can't do anything.

In particular, you know that the measured value of a qubit drawn from a probability distribution constructed by some quantum algorithm. The algorithm will, presumably, construct a distribution that's quite tightly concentrated about the true answer. And you can always repeat the computation to get multiple samples.

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