We report on the construction and characterization of an apparatus for quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions
are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the $S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $bar n=0.05$ and a heating rate of $dot{bar n}=0.016$ ms$^{-1}$ is measured.
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.
