Distilling Unitary Operations: A No-Go Theorem and Minimal Realization
Published in arXiv preprint, 2026
This work studies universal purification of unknown single-qubit unitaries affected by depolarizing noise. It proves that no nontrivial two-slot higher-order process can solve the task, even when indefinite causal order is allowed, and shows that three parallel slots are the minimum needed for an improvement. The optimal average fidelity for that architecture is derived analytically, together with a quantum circuit that attains it by using ancillary qubits as error-absorbing memory.