Non-Markovian noise that cannot be dynamically decoupled

1) written in a mixed style using mathematical rigor and numerical analysis

2) part of a series of papers written by this group of authors - and contains new results

1) looks like the numerical analysis has been included to make up for the lack of a solid mathematical result.

3) the counter-example is highly artificial, and the behavior displayed is not what practitioners using dynamical decoupling schemes would ever worry about. In fact, they would never consider the infinitely fast limit scheme which is the main mathematical focus here.

4) the discussion over the counter-example and its significance is convoluted.

5) No evidence that this is actually a "folklore"

6) the non-Markovian model considered here is trivially a single particle - I suspect the authors are using the term non-Markovian as it sounds flashy and suggests a stronger result than mere Markovian models. The reverse is true: Markov models require infinite-dimensional heat baths and capture the properties of realistic baths which can never be captured by the primitive model considered here.

Referee report on “Non-Markovian noise that cannot be dynamically decoupled”
Authors: D. Burgarth, P. Facchi, M. Fraas, R. Hillier

Submitted to SciPost
February 2021

Dynamical decoupling is a standard technique used as a practical technique for noise suppression in physical systems. In this paper it is understood however as an idealized mathematical limit – one which cannot be realized in Nature.

The paper is one of a series by this group of authors in which they challenge conventional “physics folklore” surrounding dynamical decoupling. Unfortunately, they never point to any instances in the physics literature where this folklore is declared. Here the challenged folklore is that the so-called Zeno region provides an inherent time-scale for dynamical decoupling – but with no back up references to support this. I’m not aware of this being a concern for practitioners of dynamical decoupling.

The metier of these authors seems to be the construction of a mathematical counter-example to the perceived folklore, but frequently this will be a highly contrived model which exhibits counter-intuitive behavior in a specific and limited way, and which would never realistic arise in physics. The model of a qubit couple to a magnetic monopole considered here falls into this category.

The authors mention non-markovianity, but it is not clear what they mean by this. They seem to equate just markovianity with exponential decay. They make the emphatic claim that they "have non-Markovian noise which cannot be dynamically decoupled", but their noise model is highly artificial and it would not be a major surprise that a realistic non-Markovian environment could be constructed that does not allow their (extreme) intrepretation of dynamical decoupling.

There is also a reference to Berry’s work – but crucially no mathematical connection other than that their “numerics” shows “fractal-like” behavior. In their case the bath seems to consist of just a single particle – no one working in quantum open systems would consider such a model as a realistic source of quantum noise.

I am particularly puzzled by the following bizarre phrase in the conclusion: “While for many systems encountered in practice such reasoning is probably valid, one cannot expect to be able to prove it rigorously, because we obtained an explicit counterexample”. Surely the whole point of a counter-example is that shows immediately that a particular statement cannot be proved true! What of course they mean is that their model is an unnatural one which working physicists would dismiss as pathological.

The paper deals with themes that are not of interest to researchers working on practical dynamical coupling, and concentrates on finding unrealistic mathematical models which they claim are significant but which seem highly artificial. I cannot recommend for publication.

1) timeliness of the topic
2) mathematical rigour
3) it challenges common wisdom with a specific counterexample

1) the model analysed is somehow a toy model, most likely it can be physically simulated but it does not map straightforwardly to a ready in the lab setup.

Report on “Non-Markovian noise that cannot be dynamically decoupled”
by Daniel Burgarth, Paolo Facchi, Martin Fraas, Robin Hillier

The manuscript addresses the interplay between non markovian dynamics and effective quantum noise suppression by dynamical decoupling. Here non markovian dynamics is defined in terms of the existence of Zeno region characterized by a quadratic – rather then exponential -decay dynamics.
The general wisdom is that the existence of a Zeno region provides a timescale for an efficient dynamical decoupling. Here the authors provide a counterexample for which this is not true, namely the decoherence of a qubit coupled to a particle free to move in 1D. If the qubit is in the |0> state the particle is free, when the qubit is in the |1> state the particle feels a monopole potential at the origin. Such model, characterized by a non markovian decoherence, can be mapped
onto a system consisting of a qubit coupled to a real wave function defined on the positive real axis. The authors show that the Trotter expansion corresponding to the dynamical decoupling, obtained by fast spin flips, is unphysical for some range of hamiltonian parameters (crudely speaking, in the half line picture, the particle gets kicked out of its domain of existence).

The results are correct and they are, in my viewpoint of timely interest.

1) I found figure 2 and its caption rather obscure. Either both are made more quantitative of it would be better to drop it altogether.