= Basic measurement
{title2=$\{|b_j\rangle\langle b_j|\}_j$}
A rank-one <projective measurement> associated with an <orthonormal basis> $\{|b_j\rangle\}_j$. For a <density matrix> $\rho$, outcome $j$ has <probability> $\langle b_j|\rho|b_j\rangle$ and leaves the measured system in the <pure state> $|b_j\rangle$ whenever that <probability> is nonzero. It can be implemented by mapping this <orthonormal basis> to the <computational basis> with a <unitary transformation> and performing a <computational-basis measurement>.<The Theory of Quantum Information by John Watrous/Basic notions of quantum information>[§2.3, Definition 2.34; specialize the measurement effects to rank-one orthogonal projections]{ref}
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