  Quantum-dot based parity-to-charge conversion is a promising method for
reading out quantum information encoded nonlocally into pairs of Majorana zero
modes. To obtain a sizable parity-to-charge visibility, it is crucial to tune
the relative phase of the tunnel couplings between the dot and the Majorana
modes appropriately. However, in the presence of multiple quasi-degenerate dot
orbitals, it is in general not experimentally feasible to tune all couplings
individually. This paper shows that such configurations could make it difficult
to avoid a destructive multi-orbital interference effect that substantially
reduces the read-out visibility. We analyze this effect using a Lindblad
quantum master equation. This exposes how the experimentally relevant system
parameters enhance or suppress the visibility when strong charging energy,
measurement dissipation and, most importantly, multi-orbital interference is
accounted for. In particular, we find that an intermediate-time readout could
mitigate some of the interference-related visibility reductions affecting the
stationary limit.
