= Quantum state population
{title2=$p_k=\langle k|\rho|k\rangle$}
= Level population
{synonym}
For a chosen normalized level state $|k\rangle$, its population is the <probability> $\langle k|\rho|k\rangle=\operatorname{Tr}(|k\rangle\langle k|\rho)$ of finding the system in that state. In an orthonormal level basis these diagonal entries are nonnegative and sum to one. Off-diagonal <quantum coherence> contains information absent from the population vector, so matching all level populations need not prepare a specified coherent superposition.
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