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I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ and $(1 \,0)$ for $|0\rangle$?

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    $\begingroup$ see eg physics.stackexchange.com/q/282286/58382 $\endgroup$
    – glS
    Commented Sep 16, 2022 at 8:14
  • $\begingroup$ are you asking why is Dirac notation used in general, or are you asking why people often use the convention that $|0\rangle$ correponds to $(1,0)$ and $|1\rangle$ corresponds to $(0,1)$? $\endgroup$
    – glS
    Commented Sep 20, 2022 at 6:02

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I guess the idea of using dirac notation is pretty simple cause for qubit-- we have to define both magnitude and as well as phase.

  1. As we are going to use interference so there will be phase difference which is one kind of direction so that's another reason.
  2. As |0> and |1> is mutually exclusive and also linearly independent so we can think about column vector by representing like this-

Z-basis

  1. Also we have to remember one thing that they are normalized.
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    $\begingroup$ I am sorry but the answer is a little bit obscure and difficult to understand. Could you please elaborate more? For example, what do you mean by and another thing is suppose I assume a car just going through a track first of all if there are only two track? $\endgroup$ Commented Sep 17, 2022 at 6:36

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