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$\newcommand{\ket}[1]{|#1\rangle}$Is there some standard computational basis defined in quantum computing? Can I just call $\{\ket{0}, \ket{1}\}$ the standard computational basis?

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    $\begingroup$ Isn't it a bit redundant to call it the "standard computational" basis? I've heard it commonly called the "standard basis" (in QC and in linear algebra) and the "computational basis" (in QC), but this is the first time I'm aware of that I've seen anyone refer to "the standard computational basis". $\endgroup$ Feb 5 '19 at 19:57
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    $\begingroup$ @NieldeBeaudrap I've seen it in a couple of places. C.f. arXiv:quant-ph/0208008 (page 5). But yes, it's definitely not used much due to the redundancy. $\endgroup$ Feb 5 '19 at 20:50
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You can either call it the standard basis (as it can be mapped to the natural orthonormal basis of $\Bbb R^2$) or the computational basis, of the $2$-dimensional complex Hilbert space. The latter is more frequently used in the context of quantum computing, but you'll see mathematicians using the former more. Anyway, calling it the "standard computational" basis is simply redundant when you're dealing with $\Bbb C^2$, although I've seen some authors use it. For instance, check page 5 of From Qubits to Continuous-Variable Quantum Computation (Sanders et al., 2002).

Related: What is the Computational Basis?

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Yes, $|0\rangle$ and $|1\rangle$ is commonly called the computational basis. Some sources also call it the classical basis.

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  • $\begingroup$ You mean the standard computational basis? $\endgroup$
    – R. Chopin
    Feb 5 '19 at 19:13
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    $\begingroup$ The word "standard" is fairly superfluous. $\endgroup$
    – ahelwer
    Feb 5 '19 at 19:17

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