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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.

2 Comments:

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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