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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2$\begingroup$ see eg physics.stackexchange.com/q/282286/58382 $\endgroup$– glS ♦Sep 16, 2022 at 8:14
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$\begingroup$ 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 ♦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.
- As we are going to use interference so there will be phase difference which is one kind of direction so that's another reason.
- 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]][1] [1]: https://i.stack.imgur.com/HdvTI.png
- Also we have to remember one thing that they are normalized.
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2$\begingroup$ 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? $\endgroup$ Sep 17, 2022 at 6:36