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The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate \begin{equation} Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}. \end{equation} I've got a quick question. As $|0\rangle$ has eigenvalue $+1$ with respect to $Z$ and $|1\rangle$ has eigenvalue $-1$, according to the postulates of quantum mechanics $\pm 1$ are the results of the measurement. So why is it that in every text the results are written as $"0"$ or $"1"$? Is it simply because of a conventional correspondence $"0"\leftrightarrow +1,"1"\leftrightarrow -1$ that no one ever even bothers to write explicitly?

1I feel like this sort of misses the fundamental aspect of the matter. "0" and "1" in this context are nothing but conventional labels. We use them because they are reminiscent of how we denote bits, but we could equivalently use any other pair of symbols. – glS – 2021-02-02T10:40:08.680

1Sure. We can denote the states $|0\rangle$ and $|1\rangle$ as $| :) \ \rangle$ and $| :( \ \rangle$. – KAJ226 – 2021-02-02T11:16:07.273