Optimization of the Readout Fidelity of the Quantum State of an Optical Qubit in the 171Yb+ Ion

A scheme based on a laser cooling system has been proposed to detect the state of an optical qubit in the 171Yb+ ion. Analytical expressions have been derived for the readout fidelity including the dark photon counts and background. The parameters of the experiment have been numerically optimized to minimize the readout infidelity. The upper bound on the fidelity associated with a transient process at the beginning of the measurement procedure has been determined as 99.4%. The characteristic parameters of detection ensuring a sufficient proximity to the upper bound have been found.