Talk:Hadamard transform

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


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

— Preceding unsigned comment added by 86.142.160.167 07:16, March 8, 2008‎ (UTC)


 * Agreed. It's clear that you use this technique to take two equal-length power-of-2 numeric vectors, and generate a third vector. But, somewhere in the first paragraph, it should say WHY someone would want this third vector. My (strong) guess is that it has to do with cross-correlating the original two vectors, but that's just my guess (and a lot of Googling hasn't found any clear statement on the topic). -- Dan Griscom (talk) 11:24, 4 August 2015 (UTC)

A terrible analogy!
> 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 (talk • contribs) 11:44, 16 September 2012 (UTC)


 * Real analogies are always classical. Everything else is just defining one unknown thing relative to another unknown thing. 98.156.185.48 (talk) 03:03, 15 September 2023 (UTC)