  In order to faithfully detect the state of an individual two-state quantum
system (qubit) realized using, for example, a trapped ion or atom, state
selective scattering of resonance fluorescence is well established. The
simplest way to read out this measurement and assign a state is the threshold
method. The detection error can be decreased by using more advanced detection
methods like the time-resolved method or the $\pi$-pulse detection method.
These methods were introduced to qubits with a single possible state change
during the measurement process. However, there exist many qubits like the
hyperfine qubit of $^{171}Yb^+$ where several state change are possible. To
decrease the detection error for such qubits, we develope generalizations of
the time-resolved method and the $\pi$-pulse detection method for such qubits.
We show the advantages of these generalized detection methods in numerical
simulations and experiments using the hyperfine qubit of $^{171}Yb^+$. The
generalized detection methods developed here can be implemented in an efficient
way such that experimental real time state discrimination with improved
fidelity is possible.
