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Abstract: The quantum switch has been widely studied as a prototypical example of indefinite causal order in quantum information processing. However, the potential advantages of utilizing more general forms of indefinite causal orders remain largely unexplored. We study higher-order switches, which involve concatenated applications of the quantum switch, and we demonstrate that they provide a strict advantage over the conventional quantum switch in the task of quantum channel distillation. Specifically, we show that higher-order quantum switches enable the probabilistic distillation of any qubit Pauli channel into the identity channel with nonzero probability. This capability contrasts with the conventional quantum switch, which allows only a limited set of Pauli channels to be distilled with nonzero probability. We observe that, counterintuitively, the distillation rate generally increases the noisier the channel is. We fully characterize the asymptotic distillation rates of higher-order superswitches for qubit Pauli channels. Finally, we prove a no-go result for multiqubit generalizations.

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