In this text I’ll do some review on the definition of quantum state and quantum measurement, which was introduced here, and reasonably expand the notions into the most general instances of quantum bits.
Review Given a state $$|\psi\rangle = \sum_i \alpha_i |\varphi_i \rangle,$$ it’s possible to perform a Von Neumann measurement on the state’s space $\mathscr{H}$ with respect to the orthonormal basis $B = \{|\varphi_i \rangle\}$. The output would be a label $i$ with corresponding probability $|\alpha_i|^2$ and the system left in state $|\varphi_i\rangle$. ...