= Uniform quantum superposition
A <uniform quantum superposition> assigns the same <probability amplitude> to each <computational-basis state>. For $n$ <qubits>, there are $2^n$ such states.
The <uniform quantum superposition> of all $n$-bit strings is
$$
\frac1{\sqrt{2^n}}\sum_{x\in\{0,1\}^n}|x\rangle
=H^{\otimes n}|0\rangle^{\otimes n}.
$$
The factor $2^{-n/2}$ follows from <normalization>: $2^n$ squared amplitudes must sum to one. This state is the <product state> $|+\rangle^{\otimes n}$, so a large number of nonzero basis amplitudes does not by itself imply <entanglement>. A <computational-basis measurement> returns one string with <probability> $2^{-n}$; it does not reveal all amplitudes. <Foundations I: States and Ensembles by John Preskill>[Section 2.1, normalization, superposition and the measurement rule]{ref}
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