dan815
  • dan815
\[|V > =\frac{1+\sqrt{6}}{2\sqrt{6}}|00> + \frac{1-\sqrt{6}}{2\sqrt{6}}|01>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|10>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|11>\] http://prntscr.com/8kds95
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dan815
  • dan815
@Empty
Empty
  • Empty
cool
Empty
  • Empty
pellet why did I speak it breaks this terrible site's latex :'(

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Empty
  • Empty
Maybe we should go to the superior Peer Answer
dan815
  • dan815
lol
Empty
  • Empty
\[|V > =\frac{1+\sqrt{6}}{2\sqrt{6}}|00> + \frac{1-\sqrt{6}}{2\sqrt{6}}|01>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|10>+\frac{\sqrt{2}-\sqrt{3}}{2\sqrt{6}}|11>\] http://prntscr.com/8kds95
Empty
  • Empty
What would we do without wio's add on to make this site less trash? Like literally users are fixing the site haha.
dan815
  • dan815
tkhunny would have your head for such talk
Empty
  • Empty
I'll ban him idgaf
Empty
  • Empty
ok so what do you wanna do with this shiz son? This is a matrix basically. I'll write it out too one sec.
dan815
  • dan815
this tensor product |ij> = |i> * |j>, 1<=i,j<=2 whats that about
dan815
  • dan815
does this first mean that i and j are 2 by 2 matrces and we take tensor product of these 2 matrices?
dan815
  • dan815
or are they 2 vectors of dimension 2
dan815
  • dan815
|dw:1443201862130:dw|
dan815
  • dan815
like that?
Empty
  • Empty
Nah not quite.
Empty
  • Empty
\[|ij \rangle = |i \rangle \otimes |j \rangle \] 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
dan815
  • dan815
wait an outer product always produces an operator right
dan815
  • dan815
|dw:1443202519738:dw|
Empty
  • Empty
Yeah, all you're doing is this: |dw:1443202706547:dw|
dan815
  • dan815
ok i gotcha
dan815
  • dan815
would that thing you did there be the tensor product of the 2 vectors i and j defined above
dan815
  • dan815
where that matrix can be rewritten as ac|11> + ad|12>+bc|21> +bd |22>
dan815
  • dan815
i dont think that matrix can be rewritten like this nevermind
dan815
  • dan815
se this would be like one of those column vectors they keep using for 4 states
dan815
  • dan815
okay so basically a tensor product is just this diract notation for a matrix
Empty
  • Empty
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: \[| ij \rangle = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = a|00\rangle + b |01 \rangle +c |10 \rangle + d | 11 \rangle\]
Empty
  • Empty
At least I think so, I might be mixing the notation up possibly.
dan815
  • dan815
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
dan815
  • dan815
http://prntscr.com/8keczo
dan815
  • dan815
wait okay before that question so supppose i just write it out like this 2 by 2 matrix
dan815
  • dan815
|dw:1443204170570:dw|
dan815
  • dan815
http://prntscr.com/8kejen
dan815
  • dan815
i better go eat

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