  A parity measurement on two qubits, each consisting of a single atom in a
cavity, can be realized by measuring the phase shift of a probe beam, which
interacts sequentially with the two qubits, but imperfections lead to
decoherence within the subspaces of a given parity. We demonstrate that a
different setup, where the probe light interacts repeatedly with the qubits,
can reduce the rate of decoherence within the odd or the even parity subspace
significantly. We consider both the case of a resonant and the case of a
nonresonant light-atom interaction and find that the performance is comparable
if the parameters are chosen appropriately.
