Some general results on dynamical decoupling

We analyze the efficacy of dynamical decoupling in suppressing decoherence using the time-expansion of the noise correlations. We prove that when the time-expansion of the noise correlations has odd power terms, the dynamical decoupling cannot eliminate the decoherence to an arbitrary order of the short time. And we also show that for noise without hard high-frequency cut-off, the Carr-Purcell-Meiboom-Gill sequences are the optimal solution in the short-time limit.