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)