We investigate the distinguishability of qubits governed by \(\mathcal{P}\mathcal{T}\) - and \(\mathcal{A}\mathcal{P}\mathcal{T}\) -symmetric Hamiltonians in both unbroken and broken phases. Analytical expressions for the time-dependent distinguishability are derived, showing that in the unbroken phase, both systems exhibit periodic oscillations. The oscillation period decreases with increasing Hermitian parameters or with decreasing non-Hermitian contributions, and the distinguishability reaches unity at integer multiples of this period. This work extends earlier studies on \(\mathcal{P}\mathcal{T}\) -symmetric qubits by exploring more general \(\mathcal{P}\mathcal{T}\) -symmetric Hamiltonians and by incorporating \(\mathcal{A}\mathcal{P}\mathcal{T}\) -symmetric qubits into the analysis.
