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One of the one-qbit simple quantum gate is X which defined by:

X: |0> ----- |1>

|1> ----- |0>

but how does this gate ( unitary operator ) act on |i> state? (i=0 or 1)

I mean at first we have to measure what state is ( 0 or 1) and so flip them but after we know the state, it will calapse to |0> or |1>.

so X|i>=|-i> is not correct according what I said.

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# One-qbit quantum gates

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