Highly state-selective, weakly dissipative population transfer is used to irreversibly move the population of one ground state qubit level of an atomic ion to an effectively stable excited manifold with high fidelity. Subsequent laser interrogation accurately distinguishes these electronic manifolds, and we demonstrate a total qubit state preparation and measurement (SPAM) inaccuracy $epsilon_mathrm{SPAM} < 1.7 times 10^{-4}$ ($-38 mbox{ dB}$), limited by imperfect population transfer between qubit eigenstates. We show experimentally that full transfer would yield an inaccuracy less than $8.0 times 10^{-5}$ ($-41 mbox{ dB}$). The high precision of this method revealed a rare ($approx 10^{-4}$) magnetic dipole decay induced error that we demonstrate can be corrected by driving an additional transition. Since this technique allows fluorescence collection for effectively unlimited periods, high fidelity qubit SPAM is achievable even with limited optical access and low quantum efficiency.
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