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

### Submission summary

 As Contributors: Daniel Burgarth · Paolo Facchi Arxiv Link: https://arxiv.org/abs/1904.03627v5 (pdf) Date accepted: 2021-07-20 Date submitted: 2021-07-09 02:43 Submitted by: Burgarth, Daniel Submitted to: SciPost Physics Academic field: Physics Specialties: Mathematical Physics Quantum Physics Approach: Theoretical

### Abstract

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

Published as SciPost Phys. 11, 027 (2021)

Dear Editor,

Thank you for your message. We have implemented all minor revisions to the referees as suggested. In particular, we have amended the title and clarified the remark about magnetism in 1D as requested by Referee 2, and have added a comment about the back-action of DD along the lines of Referee 3. Referee 1 did not suggest edits. We thank the referees for helping to make our statements more precise.

Kind regards, the Authors

### List of changes

* Title changed from "Non-Markovian noise that cannot be dynamically decoupled" to "Non-Markovian noise that cannot be dynamically decoupled by periodic spin echo pulses".

* Abstract modified accordingly, "even though the system shows a quadratic decay (a Zeno region revealing non-Markovian noise), it cannot be decoupled, no matter how fast the rotations." becomes "even though the system shows a quadratic decay (a Zeno region revealing non-Markovian noise), it cannot be decoupled by periodic spin echo pulses, no matter how fast the rotations.".

*Added "This qualitative picture might have implications for other systems, too. For example, to dynamically decouple an interacting bath prepared in a low-energy state, one should design the dynamical decoupling such that it would not cause the excitations of high-energy modes or the decoupling scheme could be spoiled." at the end of Section 4.

* Changed sentence in conclusion to "Finally our model shows that in the time-dependent case, not all dynamical effects of quantum magnetism on $L^2(\mathbb{R})$ can be removed by gauge transformations [24]" to distinguish it from one-dimensional spin physics.