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

The factor $2^{-n/2}$ follows from normalization: $2^n$ squared amplitudes must sum to one. This state is the product state $|+{⟩}^{\otimes n}$, 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. ^[ref]