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## Main Question or Discussion Point

Hey folks, I have a pretty simple quantum information question that I was hoping somebody could answer.

let's say I have a pure state \ket{\psi} = \alpha \ket{10} + \beta \ket{11} + \gamma \ket{01} + \theta \ket{00}.

I then perform a measurement on only the first qubit and observe a value of 1. How do I now represent the state of my system? The temptation is to just renormalize the coefficients \alpha and \beta, but it's not clear to me whether this is correct or whether I have to use a density operator. Any advice would be awesome, this is a question that popped up while I was reading N and C for self-study. Thanks for your time!

let's say I have a pure state \ket{\psi} = \alpha \ket{10} + \beta \ket{11} + \gamma \ket{01} + \theta \ket{00}.

I then perform a measurement on only the first qubit and observe a value of 1. How do I now represent the state of my system? The temptation is to just renormalize the coefficients \alpha and \beta, but it's not clear to me whether this is correct or whether I have to use a density operator. Any advice would be awesome, this is a question that popped up while I was reading N and C for self-study. Thanks for your time!