Dynamical decoupling for a qubit in telegraphlike noises

Based on the stochastic theory developed by Kubo and Anderson, we present an exact result of the decoherence function of a qubit in telegraphlike noises under dynamical decoupling control. We prove that for telegraphlike noises, the decoherence can be suppressed at most to the third order of the time and the periodic Carr-Purcell-Merboom-Gill sequences are the most efficient scheme in protecting the qubit coherence in the short-time limit.