Talk:Hadamard transform

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What's missing from the page is a brief description of what these mean. Why are the these results interesting?

H|1\rangle = \frac{1}{\sqrt{2}}|0\rangle-\frac{1}{\sqrt{2}}|1\rangle.
H|0\rangle = \frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle.
H( \frac{1}{\sqrt{2}}|0\rangle-\frac{1}{\sqrt{2}}|1\rangle )= \frac{1}{2}( |0\rangle+|1\rangle) - \frac{1}{2}( |0\rangle - |1\rangle) = |1\rangle ;
H( \frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle )= \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle) + \frac{1}{\sqrt{2}}( \frac{1}{\sqrt{2}}|0\rangle-\frac{1}{\sqrt{2}}|1\rangle)= |0\rangle .

A terrible analogy![edit]

> This would be like taking a fair coin that is showing heads, flipping it twice, and it always landing on heads after the second flip.

This is a terrible analogy! Flipping a coin implies observation of the result. Had we used Hadamard transform for flipping a coin, the subsequent flips would not be any different. Quantum effects should never be explained using classical analogies! — Preceding unsigned comment added by Kallikanzarid (talkcontribs) 11:44, 16 September 2012 (UTC)