= Pseudo-pure state
{title2=$\rho=(1-p)I/d+p|\psi\rangle\langle\psi|$}
A mixture of the maximally mixed state and a chosen pure state. Unitary conjugation preserves its identity part; every traceless observable has expectation $p\langle\psi|O|\psi\rangle$. The coefficient $p$ is effective polarization rather than literal purity: $\operatorname{tr}\rho^2=1/d+(1-1/d)p^2$. Preserving the largest population of $n$ weakly polarized equal spins and averaging the rest gives $p\simeq n\epsilon/[2(2^n-1)]$, displaying the signal penalty of this high-temperature ensemble preparation.
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