  We present rigorous performance bounds for the quadratic dynamical decoupling
(QDD) pulse sequence which protects a qubit from general decoherence, and for
its nested generalization to an arbitrary number of qubits. Our bounds apply
under the assumption of instantaneous pulses and of bounded perturbing
environment and qubit-environment Hamiltonians such as those realized by baths
of nuclear spins in quantum dots. We prove that if the total sequence time is
fixed then the trace-norm distance between the unperturbed and protected system
states can be made arbitrarily small by increasing the number of applied
pulses.
