Simon coset state
= Simon coset state
{c}
{title2=$(|x\rangle+|x\oplus s\rangle)/\sqrt2$}
In <Simon's algorithm>, conditioning on a function value leaves the first <quantum register> in an equal coherent sum of its two <preimages>. This is a <pure state>, even though discarding the second <quantum register> without retaining its outcome generally leaves a <mixed state>. The label $x$ depends on the measured value; the period $s$ does not.