Adiabatic state distribution using anti-ferromagnetic spin systems

1 - The manuscript is written in a precise and clear language;
2 - It features an in-depth discussion over the necessary ingredients for carrying out a adiabatic quantum-state transfer and entanglement distribution in arbitrary graphs;
3 - It makes a significant contribution to the field of adiabatic quantum communication in general.

1 - Although the work is pretty much self-contained, there is only one practical example by the end of manuscript;
2 - The literature of 'quantum communication in spin chains' (which is enormous) is not well addressed.

The author outlines the key elements to perform adiabatic quantum communication tasks through a Heisenberg chain, wherein the involved parties are assumed to have
full control over a small set of couplings. Two protocols are particularly addressed, namely quantum-state transfer and entanglement distribution and a practical (numerical) example is provided using star graphs. The author also discusses limitations of the method and some possible experimental realizations.

I think the results are relevant and the theoretical reasoning behind them is very well presented. Also, it generalizes some previous results on adiabatic quantum communication protocols to arbitrary graphs. Therefore, for those reasons and given the overall quality of the work, I recommend it for publication.

I would only ask the author to: (1) explore a bit more the literature of
'quantum communication in spin chains' in the 'Introduction', that is to mention what are the main schemes put forward so far. A brief look at Refs [2] and [3] (and references within) is helpful; and (2) explain how exactly the results in Ref. [7] are generalized, as stated in Sec. 3.2.

1 - To explore a bit more the literature of 'quantum communication in spin chains' in the 'Introduction';
2 - To explain how exactly the results in Ref. [7] are generalized, as stated in Sec. 3.2.

1- Although I am not going to require the authors to add this, it might have been nice to see some more cases analyzed numerically, including possibly cases which work but cannot rigorously be shown to work by the results in the earlier sections

2- There are some minor issues with some of the plots, as discussed in the requested changes

The authors have done a detailed analysis of quantum state transfer and entangelment distribution on general graphs using sytems with anti-ferromagnetic Heisenberg interactions. The majority of the paper is devoted to discussing the theory around when this can and cannot be done, including both examples when it can, and counter-examples where some key assumptions do not hold and the transfer protocols do not work. The authors have also included a brief section with numerical analysis on a specific system, and discussion of possible experimental implementations. Overall, I think this paper is quite good, mathematically correct as far as I can tell, and represents a contribution to the field. I therefore think this paper should be published, with only minor changes, as discussed below.

The paper is clearly written and there are high quality cartoon figures to help explain the concepts.

minor changes:

The color bar on Fig. 6 is not labeled, while this is explained in the caption, it should also be labeled to make the figure more clear to the reader

Some energy levels are missing from the top of Fig. 5, while it is clear to a reader familiar with matrix numerics that more levels are not shown at the top, it would still make the figure more visually appealing to include all levels which would be visible on the plot.

I find it odd that the abstract only mentions some of the results, the discussion of experimental implementations and on different error types should be mentioned in the abstract, as these are important parts of the paper.

1- The color bar on Fig. 6 is not labeled, while this is explained in the caption, it should also be labeled to make the figure more clear to the reader

2- Some energy levels are missing from the top of Fig. 5, while it is clear to a reader familiar with matrix numerics that more levels are not shown at the top, it would still make the figure more visually appealing to include all levels which would be visible on the plot.

3- I find it odd that the abstract only mentions some of the results, the discussion of experimental implementations and on different error types should be mentioned in the abstract, as these are important parts of the paper.