Arcadian Functor

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Marni D. Sheppeard

Thursday, October 02, 2008

M Theory Lesson 231

Let us relabel the $M_{i}$ as $X$, $Y$, $Z$ and $T$. Then the analogue of the quandle relations for the binary Lie bracket in the Pauli case are the cyclic ternary relations

$X = ZYTZ$
$Y = TZXT$
$Z = XTYX$
$T = YXZY$

which are easily verified by multiplying out the matrices. Note also how the two dual pairs yield the quantum plane relations

$YX = \omega XY = \omega (312)$
$TZ = \omega ZT = \omega (231)$

There are also other relations of this type. So the Lie bracket is not the natural structure to study for three dimensional quantum information.


Blogger L. Riofrio said...

Just got around to reading your paper on "dark flow." Thanks for the citation!

October 03, 2008 9:02 AM  
Blogger Kea said...

Well, it's not exactly a paper, but thanks. I am not giving up applying for postdocs.

October 03, 2008 1:41 PM  

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