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Dynamical decoupling is the leading technique to remove unwanted interactionsin a vast range of quantum systems through fast rotations. But what determinesthe time-scale of such rotations in order to achieve good decoupling? Byproviding an explicit counterexample of a qubit coupled to a charged particleand magnetic monopole, we show that such time-scales cannot be decided by thedecay profile induced by the noise: even though the system shows a quadraticdecay (a Zeno region revealing non-Markovian noise), it cannot be decoupled byperiodic spin echo pulses, no matter how fast the rotations.

Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses