Quantum physics does not allow us to access all this information directly, however. A measurement will yield only one of all possible values, destroying all others. If not for the no cloning theorem, we could first measure formula_64 without measuring formula_63, and then make a few copies of the resulting state (which is a superposition of states all having the same formula_64). Measuring formula_63 on these states would provide different formula_63 values which give the same formula_64, leading to the period. Because we cannot make exact copies of a quantum state, this method does not work. Therefore, we have to carefully transform the superposition to another state that will return the correct answer with high probability. This is achieved by the quantum Fourier transform.