Dynamics of Majorana tetron qubits under quasiparticle poisoning

We study the dissipative dynamics of a Majorana tetron qubit in the presence of extrinsic quasiparticle poisoning due to the coupling to external leads. From the Bloch-Redfield equation describing a finite-size topological superconductor hosting four Majorana zero modes, we recover analytical expressions for the steady state, the parity leakage rate, and the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the dephasing rate is gradually removed by the energy splitting of the qubit states. These results can be useful to understand time-domain experimental data in Majorana qubit prototypes.