= Quantum superposition
{title2=$|\psi\rangle=\sum_j a_j|j\rangle,\quad\sum_j|a_j|^2=1$}
A normalized <quantum state> is a <linear combination> of <orthonormal basis> vectors in a <Hilbert space>. Its <density operator> is $|\psi\rangle\langle\psi|$. When at least two basis amplitudes are nonzero, it has off-diagonal terms and differs from the <mixed state> $\sum_j|a_j|^2|j\rangle\langle j|$. <Quantum gates> act linearly on this superposition and preserve its phase information.
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