\[|V > =\frac{1+\sqrt{6}}{2\sqrt{6}}|00> + \frac{1-\sqrt{6}}{2\sqrt{6}}|01>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|10>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|11>\] http://prntscr.com/8kds95

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\[|V > =\frac{1+\sqrt{6}}{2\sqrt{6}}|00> + \frac{1-\sqrt{6}}{2\sqrt{6}}|01>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|10>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|11>\] http://prntscr.com/8kds95

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cool
pellet why did I speak it breaks this terrible site's latex :'(

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Maybe we should go to the superior Peer Answer
lol
\[|V > =\frac{1+\sqrt{6}}{2\sqrt{6}}|00> + \frac{1-\sqrt{6}}{2\sqrt{6}}|01>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|10>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|11>\] http://prntscr.com/8kds95
What would we do without wio's add on to make this site less trash? Like literally users are fixing the site haha.
tkhunny would have your head for such talk
I'll ban him idgaf
ok so what do you wanna do with this shiz son? This is a matrix basically. I'll write it out too one sec.
this tensor product |ij> = |i> * |j>, 1<=i,j<=2 whats that about
does this first mean that i and j are 2 by 2 matrces and we take tensor product of these 2 matrices?
or are they 2 vectors of dimension 2
|dw:1443201862130:dw|
like that?
Nah not quite.
\[|ij \rangle = |i \rangle \otimes |j \rangle \] i and j can each take on 0 or 1 to give you entries of a matrix. It might be easier to imagine taking the product of two vectors to make a matrix: \[A_{ij} = x_iy_j^\dagger\] Notice that this is like the dot product but flipped backwards so that it creates a matrix. This is called the outer product as opposed to the dot product which is an inner product. :P
wait an outer product always produces an operator right
|dw:1443202519738:dw|
Yeah, all you're doing is this: |dw:1443202706547:dw|
ok i gotcha
would that thing you did there be the tensor product of the 2 vectors i and j defined above
where that matrix can be rewritten as ac|11> + ad|12>+bc|21> +bd |22>
i dont think that matrix can be rewritten like this nevermind
se this would be like one of those column vectors they keep using for 4 states
okay so basically a tensor product is just this diract notation for a matrix
well ok so really all this does is take the hermitian conjugate: \[|i \rangle^\dagger = \langle i| \] Also I realize that this stuff is pretty confusing since it has a lot of overlap of notation for stuff. Here we're looking at: \[| ij \rangle = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = a|00\rangle + b |01 \rangle +c |10 \rangle + d | 11 \rangle\]
At least I think so, I might be mixing the notation up possibly.
ya im looking through the book they are reseving this tensor product strictly for like a matrix and that way of writing http://prntscr.com/8ke94r for like your column matrices only like if u look at page 25 example 2.2.4
http://prntscr.com/8keczo
wait okay before that question so supppose i just write it out like this 2 by 2 matrix
|dw:1443204170570:dw|
http://prntscr.com/8kejen
i better go eat

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