Fig. 4: Results of quantum process tomography.
From: Single ion qubit with estimated coherence time exceeding one hour
a Red and blue points represent process and mean fidelities, respectively. Error bars are standard deviations. The red line is the fitting result of Eq. (1). The blue line is the fitting result of the exponential decay function. Inset shows extrapolations of fits in a longer time range. The shadow indicates the enlarged area in the figure. The red and blue dashed horizontal lines indicate the process fidelity and mean fidelity of the final state, where the system lost all the quantum information. The blue vertical line indicates the time point when mean fidelity decays to 1/e threshold. (b), The real part of the process matrix after a storage time of (i): 4 min, (ii): 8 min, and (iii): 16 min. The largest diagonal element of the process matrix is the identity operation part, \({\chi }_{11}^{\exp }\), which is the process fidelity Fp. (c), State evolution represented in the Bloch sphere after a storage time of (i): 4 min, (ii): 8 min, and (iii): 16 min. Gray meshed spheres represent the initial pure states, which form the Bloch sphere. And blue spheres represent the output states after corresponding storage time, which are the same as the input state at T = 0 but shrink into the Bloch sphere later and transition to a dot in the center for \(T\gg \min ({T}_{1},{T}_{2})\). Given the input state, the corresponding output state is calculated by the process matrix \({\chi }^{\exp }\).
