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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

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  1. dan815
    • one year ago
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    @Empty

  2. Empty
    • one year ago
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    cool

  3. Empty
    • one year ago
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    pellet why did I speak it breaks this terrible site's latex :'(

  4. Empty
    • one year ago
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    Maybe we should go to the superior Peer Answer

  5. dan815
    • one year ago
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    lol

  6. Empty
    • one year ago
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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

  7. Empty
    • one year ago
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    What would we do without wio's add on to make this site less trash? Like literally users are fixing the site haha.

  8. dan815
    • one year ago
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    tkhunny would have your head for such talk

  9. Empty
    • one year ago
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    I'll ban him idgaf

  10. Empty
    • one year ago
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    ok so what do you wanna do with this shiz son? This is a matrix basically. I'll write it out too one sec.

  11. dan815
    • one year ago
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    this tensor product |ij> = |i> * |j>, 1<=i,j<=2 whats that about

  12. dan815
    • one year ago
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    does this first mean that i and j are 2 by 2 matrces and we take tensor product of these 2 matrices?

  13. dan815
    • one year ago
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    or are they 2 vectors of dimension 2

  14. dan815
    • one year ago
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    |dw:1443201862130:dw|

  15. dan815
    • one year ago
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    like that?

  16. Empty
    • one year ago
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    Nah not quite.

  17. Empty
    • one year ago
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    \[|ij \rangle = |i \rangle \otimes |j \rangle \] 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

  18. dan815
    • one year ago
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    wait an outer product always produces an operator right

  19. dan815
    • one year ago
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    |dw:1443202519738:dw|

  20. Empty
    • one year ago
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    Yeah, all you're doing is this: |dw:1443202706547:dw|

  21. dan815
    • one year ago
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    ok i gotcha

  22. dan815
    • one year ago
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    would that thing you did there be the tensor product of the 2 vectors i and j defined above

  23. dan815
    • one year ago
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    where that matrix can be rewritten as ac|11> + ad|12>+bc|21> +bd |22>

  24. dan815
    • one year ago
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    i dont think that matrix can be rewritten like this nevermind

  25. dan815
    • one year ago
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    se this would be like one of those column vectors they keep using for 4 states

  26. dan815
    • one year ago
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    okay so basically a tensor product is just this diract notation for a matrix

  27. Empty
    • one year ago
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    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: \[| ij \rangle = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = a|00\rangle + b |01 \rangle +c |10 \rangle + d | 11 \rangle\]

  28. Empty
    • one year ago
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    At least I think so, I might be mixing the notation up possibly.

  29. dan815
    • one year ago
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    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

  30. dan815
    • one year ago
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    http://prntscr.com/8keczo

  31. dan815
    • one year ago
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    wait okay before that question so supppose i just write it out like this 2 by 2 matrix

  32. dan815
    • one year ago
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    |dw:1443204170570:dw|

  33. dan815
    • one year ago
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    http://prntscr.com/8kejen

  34. dan815
    • one year ago
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    i better go eat

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