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To measure, observe that you are simply projecting a quantum state onto some basis set of vectors. First, I will note that this state is not normalized. Let us first define the following quantum state.
$$|\psi_i\rangle = \begin{pmatrix}1\\-1\\0\\0\end{pmatrix}.$$
Then, calculating the corresponding probability yields:
$$|\langle \psi_i|\psi_i\rangle|^2 = (...
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