Fig. 4: Fidelity (F1∣2) of preserving ion1 for detection light at ion2 location.
a F1∣2 vs polarization of the detection probe light, showing that it is maximized for probe light with no π − polarization. The dashed line represents the optimal polarization31 for the process qubit (ion2) state-detection. The dotted line represents the polarization used to measure F1∣2 in figures b, c. Measured values of F1∣2 at d = 4w, shown in figures a–c, are for detection probe light of intensity I = 1.25(16)Isat applied for τd= 11 μs. Error bars in figures a–c denote standard deviation in estimating F1∣2, using 20 bootstrapping repetitions from 200 measurements (Supplementary Note 7). The estimated infidelity (1-F1∣2) due to the inherent decoherence of the qubit in the absence of the probe light is < 3 × 10−5. b F1∣2 vs the distance d (case-B in Fig. 2b). For comparing the crosstalk IX, we measure F1∣2 for a probe beam with relative intensity attenuated to 7.2(2) × 10−5 addressing ion1 (triangle marker at d = 0). For comparison, F1∣2 is calculated(solid gray line) for a diffraction-limited (Numerical Aperture NA = 0.16) Gaussian beam of beam waist w. F1∣2 fidelity is > 99.6% for d≥4w. c Measured F1∣2 for various shifted locations of the ion from the center of the field of view (FOV). Here the center of FOV denotes the location at which the aberrations have been characterized and compensated (see Methods). F1∣2 is preserved for a large FOV of 460 μm. d Calculated process qubit (ion2) detection fidelity13,30 (Supplementary Note 6) and asset qubit(ion1) preservation fidelity (F1∣2) as the function of τd (detection time). Here, for estimating the process qubit (ion2) detection fidelity, we assume that the process qubit is illuminated with a detection beam of I2 = Isat with optimal polarization and a measurement apparatus of net detection efficiency of 4%, compatible with the state-of-the-art experiments. We employ a photon count thresholding method to differentiate between \(\left\vert \uparrow \right\rangle\) and \(\left\vert \downarrow \right\rangle\) states. Furthermore, we use an algorithm that completes the detection process upon measuring the first photon, reducing detection time by a factor of 213,41,42. For estimating F1∣2, we assume intensity crosstalk of IX = 5 × 10−5, I2 = Isat, and optimal polarization for the process qubit state-detection. The vertical line at τd ≈ 8.5 μs represents the optimal detection time that maximizes the product of these two fidelities. e Optimal detection time (opt. τd) as a function of the net detection efficiency of the measurement apparatus.
