  We demonstrate high-fidelity Zeeman qubit state detection in a single trapped
88 Sr+ ion. Qubit readout is performed by shelving one of the qubit states to a
metastable level using a narrow linewidth diode laser at 674 nm followed by
state-selective fluorescence detection. The average fidelity reached for the
readout of the qubit state is 0.9989(1). We then measure the fidelity of state
tomography, averaged over all possible single-qubit states, which is 0.9979(2).
We also fully characterize the detection process using quantum process
tomography. This readout fidelity is compatible with recent estimates of the
detection error-threshold required for fault-tolerant computation, whereas
high-fidelity state tomography opens the way for high-precision quantum process
tomography.
