Tapping into Permutation Symmetry for Improved Detection of k-Symmetric Extensions
Round 1
Reviewer 1 Report
By using an improved semi-definite programming the authors study the detection of k-symmetric extensions. It is shown that this method diminishes the searching space dimensionality and trims the number of parameters essential for positive definiteness tests. Detailed discussions are given to the 2 and 3-qutrit case. The results could be considered for publication.
Reviewer 2 Report
entropy-2635205-peer-review-v1
The authors study the implementation of symmetric extensions for probing correlations of entangled quantum system. Also, the technique appears to diminish the dimensionality of the search space and reduce the number of parameters
for the positive definiteness tests. Overall, the paper is well written and it should be accepted for publication. As a side remark, I like the way the abstract and part of the introduction is worded. It exudes scholarly understanding of the subject.
I have not checked all the calculations nor the optimization algorithm in the study. However, I believe that they are correctly presented. The authors have also compared their running time with QETLAB performed on a standard laptop, AMD R7-5800H, 16 CPU cores (hyper-thread enabled), 16GB memory and showed shorter running times in their algorithm.
Overall, the article is well written, and I recommend publication without further changes.
