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dan815
 one year ago
\[V > =\frac{1+\sqrt{6}}{2\sqrt{6}}00> + \frac{1\sqrt{6}}{2\sqrt{6}}01>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}10>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}11>\]
http://prntscr.com/8kds95
dan815
 one year ago
\[V > =\frac{1+\sqrt{6}}{2\sqrt{6}}00> + \frac{1\sqrt{6}}{2\sqrt{6}}01>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}10>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}11>\] http://prntscr.com/8kds95

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Empty
 one year ago
Best ResponseYou've already chosen the best response.1pellet why did I speak it breaks this terrible site's latex :'(

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Maybe we should go to the superior Peer Answer

Empty
 one year ago
Best ResponseYou've already chosen the best response.1\[V > =\frac{1+\sqrt{6}}{2\sqrt{6}}00> + \frac{1\sqrt{6}}{2\sqrt{6}}01>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}10>+\frac{\sqrt{2}\sqrt{3}}{2\sqrt{6}}11>\] http://prntscr.com/8kds95

Empty
 one year ago
Best ResponseYou've already chosen the best response.1What would we do without wio's add on to make this site less trash? Like literally users are fixing the site haha.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0tkhunny would have your head for such talk

Empty
 one year ago
Best ResponseYou've already chosen the best response.1ok so what do you wanna do with this shiz son? This is a matrix basically. I'll write it out too one sec.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0this tensor product ij> = i> * j>, 1<=i,j<=2 whats that about

dan815
 one year ago
Best ResponseYou've already chosen the best response.0does this first mean that i and j are 2 by 2 matrces and we take tensor product of these 2 matrices?

dan815
 one year ago
Best ResponseYou've already chosen the best response.0or are they 2 vectors of dimension 2

Empty
 one year ago
Best ResponseYou've already chosen the best response.1\[ij \rangle = i \rangle \otimes j \rangle \] 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
 one year ago
Best ResponseYou've already chosen the best response.0wait an outer product always produces an operator right

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, all you're doing is this: dw:1443202706547:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.0would that thing you did there be the tensor product of the 2 vectors i and j defined above

dan815
 one year ago
Best ResponseYou've already chosen the best response.0where that matrix can be rewritten as ac11> + ad12>+bc21> +bd 22>

dan815
 one year ago
Best ResponseYou've already chosen the best response.0i dont think that matrix can be rewritten like this nevermind

dan815
 one year ago
Best ResponseYou've already chosen the best response.0se this would be like one of those column vectors they keep using for 4 states

dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay so basically a tensor product is just this diract notation for a matrix

Empty
 one year ago
Best ResponseYou've already chosen the best response.1well 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: \[ ij \rangle = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = a00\rangle + b 01 \rangle +c 10 \rangle + d  11 \rangle\]

Empty
 one year ago
Best ResponseYou've already chosen the best response.1At least I think so, I might be mixing the notation up possibly.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0ya 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
 one year ago
Best ResponseYou've already chosen the best response.0wait okay before that question so supppose i just write it out like this 2 by 2 matrix
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