Majorana qubit readout by a point-contact detector under finite bias voltages

In this work we revisit the problem of a Majorana box qubit (MBQ) readout by a point-contact (PC) detector. The logic states of the MBQ are associated with the combined fermion parities of the MBQ and its tunnel-coupled quantum dot, which is measured by a PC detector. Beyond the existing studies on limiting bias voltage regimes, we analyze the steady-state current and the current power spectrum across all bias voltages. Our results indicate that the MBQ readout via the parity-dependent detector current is effective only at low bias voltage regime and requires the dot energy level to be off-resonance with the Majorana qubit. In contrast, the current power spectrum allows MBQ readout through the parity-dependent Rabi oscillation peak signals for arbitrary bias voltages, without restrictions on the dot energy level. Particularly, with focus on the MBQ measurement visibility, we analyze the peak-to-pedestal ratio for each characteristic peak (associated with each logic state of the qubit) and the signal-to-noise ratio of the two peaks. By examining these two metrics, we identify the optimal bias voltage window for the PC detector at low temperature limit.