Non-Markovianity induced by Pauli twirling

Abstract Noise forms a central obstacle to effective quantum information processing. Recent experimental advances enable noise tailoring through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This is essential for fault-tolerant quantum computation, noise characterization, and error mitigation. Pauli-Lindblad channels aptly parameterize quasi-local Pauli channels, where negative Pauli-Lindblad parameters have been excluded on the basis of Markovianity of the noise processes. We study how Pauli twirling affects Markovianity using two established notions, which we term channel semigroup Markovianity for channels and Markovianity by divisibility for channel families. We prove that (1) any Pauli channel with nonzero Pauli eigenvalues admits a Pauli-Lindblad parameterization if complex Pauli-Lindblad parameters are allowed, and (2) a Pauli channel with strictly positive and nondegenerate eigenvalues fails to be channel semigroup Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Pauli twirling can break channel semigroup Markovianity, even when the underlying noise process is Markovian by divisibility, an important example being the standard implementation of the $$\sqrt{X}$$ X gate. Thus, allowing negative or even nonreal Pauli-Lindblad parameters is necessary for correct noise descriptions in experimentally relevant scenarios, with direct implications for quantum error mitigation protocols that rely on accurate noise characterization.