  The $\textit{omg}$ protocol is a promising paradigm that uses multiple,
application-specific qubit subspaces within the Hilbert space of each single
atom during quantum information processing. A key assumption for $\textit{omg}$
operation is that a subspace can be accessed independently without deleterious
effects on information stored in other subspaces. We find that intensity noise
during laser-based quantum gates in one subspace can cause decoherence in other
subspaces, potentially complicating $\textit{omg}$ operation. We show, however,
that a magnetic-field-induced vector light shift can be used to eliminate this
source of decoherence. As this technique requires simply choosing a certain,
magnetic field dependent, polarization for the gate lasers it is
straightforward to implement and potentially helpful for $\textit{omg}$ based
quantum technology.
